CaptainCoulson

Personally, I would say natural/training is the same as any other forms, *except* it comes mostly from your own skills and not any kind built-in superpowers, or strange effect that changed you, or even being a normal person except for having a gadget or artefact or gift of power from a wizard.
 
Shazam/Captain Marvel? Magic. Got given alternate form of immense power and the associated skill with magic as a result.
 
Thor? Magic. Got born with superpowers compared to humans because of being magical in nature. Also, gifted with Mjolnir.
 
But Doctor Strange? Natural/Training. He wasn't born a god, he wasn't gifted with a bunch of superpowers by an immortal and nobody left him a magical artefact. His dedication to study, meditation, practice, and eventually to defending the world, led Doctor Strange to become skilled with the spells and rites and invocations that grant him his incredible "powers".
 
Cyborg? Technology. His body is rebuilt as something new, using a fusion of human and the advanced technology that now is his body.
 
Green Lantern? Technology. He was gifted with the Green Lantern ring, an extremely advanced piece of alien technology under his command.
 
Iron Man? Natural/Training. Tony Stark has honed his genius intellect and advanced purely human technology to a level that is comparable to many alien empires.
 
The X-Men? Mutants. They have been born with an advanced, superhuman physiology that blesses them all with superpowers.
 
The Inhumans? Mutants. They suffered an exposure to terrigen mists that mutated in their DNA to give them superpowers.
 
Hourman? Natural/Training. He uses his incredible intellect and thorough education in chemistry, and biochemistry, to produce Miraclo, the one hour superpower pills that grant him superpowers for one hour at a time, letting him perform great heroics.
 
And so on.
 
Basically, whatever your superpower is, you can potentially get there with your own skills and talents, and therefore be a Natural/Training based superhero... Or, you can get lucky, and stumble on them, in which case you have to use a different type of origin story to explain.
 
Basically, I think that the important part is the fact that these heroes are who they are without their powers.
 
If Billy Batson couldn't change forms, he is just a human child. Thor used to turn into Donald Blake regularly, and always needed to change back into Thor before he was a significant threat to his enemies. Meanwhile, Doctor Strange had a long story arc recently that centred entirely on him *losing* his magic, but still finding ways to be just as effective without them, because he knows his enemies strengths and weaknesses.
 
If Green Lantern loses his ring, he is just a man. Potentially, depending on the Green Lantern, a military officer, but still just a man. Take away the suit from War Machine, and he, too, is just a military officer. But take the suit away from Tony Stark, and what is he? A billionaire, genius, playboy, philanthropist. Heck, if he can find a cave and a box of scraps, then a few days later, he'd have another Iron Man suit.
 
Inject a mutant with "the cure" and what do you get? Functionally humans, although technically just still mutants with a dormant X-gene that can still be triggered again. Cure inhumans? They become humans. Dose Hourman with some new "antidote" to miraclo? He'll just take another dose and get another hour of superpower.

Booked to see it this week coming. The latest of The Rock's amazing career of Jungle Adventure Pulp Films. Starting to feel like The Rock has the same taste in films as I do.

Sounds like a fun addition to a game. Plenty of people use nazi soldiers and mafia henchmen as classic pulp bad guys, so a little variety ripped right out of the headlines from that era sounds great!
 
Well, since you're asking here, you're clearly playing a pulp action-adventure game, so I'd lean towards them being somewhat skilled but also having fairly potent weapons and a pretty good car (speedy, yet manoeuverable, but also reasonably tough) and then also add a heaping helping of plain old luck on top (good luck for them, and maybe bad luck for anybody trying to stop them).
 
Basically I would try to make them seem like significant threats to normal civilians and even less combat-focussed heroes, but not enough to stand up to an enemy military (Nazi invaders, or an alien war robot or the like) by themselves. 

Honestly, I'm starting to wonder about some people becoming super, not because of their own efforts, strictly speaking, but because they're the sort of people that an enterprising super-scientist/magic-user is likely to decide might make for a good hero and therefore they end up gifted with some advancedbtechnology or mystical artefacts or super-soldier serum or some arcane empowerment. 
 
Like, we'd end up with Dwayne Johnson and Keanu Reeves showing up to join the world-saving superhero team, festooned with magical artefacts and wearing power armour, but even if you took all the gadgets and magic items away, they still turn out to be full of healing factors and superstrength and casting spells. All on the basis that the two of them have a reputation as really nice people, who are very physically capable.

Potion of Slippery Ness - Grants you a few of the more desirable qualities of famous adventurer, Slippery Ness. Makes you a bit tougher, gives you some regeneration, add a bit of a strong will, and other such things.

Hungry 
Hungry has legally changed her name to the single word, in a genuine tribute to the single word adjective monikers of Disney's seven dwarves.  
 
From her father, a wealthy crimelord, she has inherited a great deal of wealth, and also dwarfism. From her mother, she inherited a genius level of intelligence, a talent for engineering, and an unceasing hedonistic gluttony.
 
She has given up on walking anymore, as she prefers being "carried around like a Queen from times of yore", aboard a seat within the two metre tall war-robot that she pilots. 

The villain, provided that they have already proven somewhat capable as villains in the past, could simply offer that they will turn a new leaf and be super-heroes rather than super-villains in the future, if this scheme goes well. Or even just that they'll retire.

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Alright...
How about "The ThinkBank", a team of at least 5 wealthy genius types who, bored with their endless charity fundraisers and thinking that they could do a better job of saving the world if only they were running everything, devote their genius, and cash, toward attempting the thrilling business of total global domination together?

I think Transform is already effectively a Cumulative power by default. The text of it describes using it again and again to make the change happen more.

Immunity to (Insert Genre You Don't Like)
 
Not sure it would be accepted in a tabletop game. Or rather, instead of actually building it into the sheet, I suspect most people are going to prefer it if you just ask ahead of a campaign that it not feature X, Y, or Z. If it was built in Hero, it would be basically a very powerful version of Transform as an area around you, big enough to cover any part of the setting you can be percieving. 
 
But, funnily enough, it does exist in DC. There is, or *was* at least, a paranormal investigator who looked into all sorts of the supernatural goings on, amd always was able to debunk them and shame the con artists behind it. In his original stories that was because his universe was a normal one. But, as the DC universe became more connected, and he was gradually sharing a world with *actual* Greek Gods and ghosts and ghouls, it was retconned into him being a metahuman who was reality warping, so the things he investigated really were real all along... until he was in range of them, at which point they turned into normal human con artistry, with all the signs of having existed as that the whole time, only to flip back to being supernatural once he'd left.
 
Personally, I'd like to try using it to make sure the campaign world was always some light-hearted family friendly adventure, not a grim, dark iron age game, or anything.
 

Having the physical capacity of a healing super-power doesn't mean that they have the psychological inclination towards, or a desire for, a position in a hospital or any of the other IRL "healer" jobs. 
 
On the other hand, having no super-power that seems very combative or whatever is no impediment at all to many, many people who have gone on to be nonpowered but still a super-hero or super-villain. You are actually already a step up the power list, as a person who *does* have super-powers.

"The Community"
Never intended to become a name, just like the classic name for the Mafia: "La Cosa Nostra" is literally just the phrase "our thing", used to refer obscurely to the crime organisation you're running. In the case of "The Community", it was a case of people involved always providing themselves with plausible deniability and even a veneer of respectability, as they do things on behalf of "The Community".
 
They don't expect you to pay for protection or anything. They simply prefer you to be a generous donor, providing the community with "necessary funding". They don't try to recruit impressionable young mutants or metahumans, to serve as lieutenants of a street gang. No, they simply welcome them to the super-powered community. And if it ends up with them implicated for, or even involved in, some initial crimes, that's just more evidence that the rest of the world is out to get people like us, and only people in The Community really have your back. The super-"heroes"? They're all just sell-outs.

Simply having the super-power of "I can heal people" doesn't make someone able or inclined to heal people in a medical sense to the exclusion of superheroics. Healing the ill or injured in a hospital is not going to stop me from putting on a costume, using a codename, and being the Superhero healer as well. Just like being Batman and Green Arrow doesn't stop Bruce Wayne funding Gotham's charities and scholarships, or in Oliver Queen's case, being Mayor. Lots of heroes have good works that they manage to balance with superheroics.
 
And, in some cases, they *wouldn't* be so suited to healing in a hospital. They maybe haven't got the patience or inclination to be a hospital healer, but they do have the psychology needed for being an active superhero. There's no reason to turn down superhero healing, just because, if this person was less suited to superhero work and more suited to hospital volunteer work, they'd save a lot of lives. They already are saving lives. Frankly, they shouldn't feel pressure to be any kind of healer. A person can be altruistic and have healing powers, but still never use their healing powers. Maybe they are very active at fundraisers for charity. A healer isn't *required* to heal, in order to be a good person. 

I see this as two different things. One, a spell that makes a roiling thundercloud in the air immediately above your head, so it can be a source for spells. Gets cast at the start of the day (or whenever you think you need to, anticipating a fight coming up), it has a form that lingers and makes it clear so it can be targeted by anti-magic powers or spells, but not a focus that could have a problem with physical or mental attacks. Two, a bunch of spells, apparently mostly storm-themed, that can only be cast if the storm cloud is overhead. 
 
That first one seems like an Endurance Reserve, with no Recovery but a nice big chunk of Endurance, made cheap because it costs some of your own Endurance to make it (but only when making it, after which it sticks around for free), it probably takes something to create it (gestures, an incantation, some kind of Magic Skill Roll, or whatever else you normally use to do a magic spell), it is percievable (that cloud of magical energy that looks like a storm), it only sticks around for however long (I said a day, could be more or less) even if it got left unused. I would personally add ability to dismiss it early, if that is not already an option. Don't want enemies stealing from my storm cloud energy for *their* magic!
 
That second one is the list of various ways you have of using this spell. They needn't be the same uses as other people who cast the same spell. You can have practised the spell itself, and be able to summon your all powerful storm of magic, only to quit study and be unable to do anything with it aside from letting it hover around your head and look cool and impressive to total idiots (an idiot being anyone with no magic). Or you may learn a bunch of ways to throw some lightning or thunder at your enemies, or a way to make the lightning within a cloud glow and pulse brightly for a while, to be a source of light for you, or a peal of loud thunder that will scare enemies, or any of the dozen ideas you've got for storm spell type effects. People who cast this spell as the base for a thorough understanding of those effects might have a dozen different "effects" as powers, all with no limitations except that it can only be powered by the Endurance Reserve of the cloud spell, as it is the only real, full spell in the list. Those who study it in passing as just an idle bit of weather magic in their much broader list of spells, might only have a single effect in a storm cloud spell repertoire, making their cloud shoot lightning, with gestures and incantations required and a magic skill roll before it will work.

There is a large sloping shadow on the wall behind the Hardy boys on the upper balcony that seems like it might be the shadow of The Shadow, wearing the distinctive cape, whilst remaining unseen.

Also, here is my Pulp Images tax.

Went to see Black Widow with the boy. He said the Red Guardian should get his own movie.  I could have done without the ham, but I sat down and thought about it. This guy is in jail thirty years, is basically out of shape, as soon as the widows call him, basically just goes "I'm out." and breaks out of the cell block. Nobody seemed to be able to take on the Taskmaster, but RG was like I can do this all day, and actually did some minor damage
CES
 
   

To be fair, if they were actually stopping crimes, even if only minor crimes and even if they would then loot the criminals, at least they were contributing to the efforts. You might resent them for taking more of the credit that they're really earning, but they do cut down on some of the work for you and the police.
 
With regards to the nature of the other team in the OP's question, I think it should depend entirely on each individual PC or NPC to choose for themselves. What do you, individually, all want from this specific group of NPCs? A major rival team to show you up when they swoop in to save the day better than you could? An enemy team who are trying to accomplish the same goals as you, before you can achieve them? Or even just a bunch of other people that you hate but you have to tolerate them? 

Very much appreciated. (Polite applause.) I suspect I might have a very grateful totally not the Sorcerer Supreme to play sometime soon, which will be wonderful. Literally. As in it is "full of wonders".

From the same film (Mystery Men), The Shoveller's one liner just before entering the climactic mission that will near certainly be a suicide mission to save the city (so it is a phrase to used about a very big, hero mission but one which will be very difficult to pull off and you might all die, or worse, fail to save the city):
 
We've got a date with destiny! And it looks like she's ordered the lobster!

I'm tempted to say that Robert Downey Jr and Chris Evans would end up being similar to their fictional counterparts. Not because of their portrayals but because of the stuff they've done outside of that.
 
In RDJ's case, visiting lots of amputees with new, advanced prosthetics. In some kind of Super-hero universe, I could see his influence in that field being able to get all sorts of hyper-advanced prosthetics, to a "winter soldier" level, ending up making lots of people into cyborg super-heroes.
 
In Chris Evans case, his crusading against the resurgence of actual Nazis, which, in a super-hero universe, means that he's going to end up as a super-hero, fighting the forces of, for example, the Red Skull.

Yeah, I've always been perfectly happy to give stories the same glossing over for the super-heroes, super-villains, super-powers and so on, that I give to police procedural stories for their 100% closure rates and to wackier sitcoms for having consequences for their shenanigans never come up.
 
When I read about the modern day and real world, except for super-powers, I accept the fact that the world is as similar to, or dissimilar from, the modern day and real world as the people who created it wanted it to be.

Ooh, nice. I really liked that when it was first on. Got a little to dramatically serious for me at times, but otherwise very good.
 
More recently, I've been watching, and just finished the latest (2nd) season of the new DC animated "Harley Quinn". I loved it! Very different interpretations of a lot of the DC world, but as long as you're on board for it, then it is a lot of great comedy and great super-hero (well, super-villain protagonist) action. 

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- the complete lyrics of the 1812 Overture
(Sorry, not sorry)