Re: Your characters, favorite by Archetype
Brick - That would be my namesake, Pariah (although he could easily fit into the Mystic category as well). He was a defrocked mage who subsequently gained superhuman strength and durability. He used his magic to augment his combat capabilities. He was scary. And he wasn't even the team's primary brick.
Energy Projector - Thunderstrike started as a naïve young college freshman who wanted to join the team just to be close to a heroine he had a crush on. He retired as an experienced, capable, and recognized member of one of the premier superteams on the planet. The evolution of his character was a lot of fun. Powerwise, he threw lightning to a lot of different effects.
Gadgeteer - To my recollection, I've never played one.
Martial Artist - Several of my characters have had martial arts packages, but none of them really fit the 'Martial Artist' archetype. I guess the closest I have is one of my current characters, Morningstar. She's a kinetic-based flier with a rather varied set of martial maneuvers. And a club.
Mentalist - Impulse was only the second character I ever built, and I player her for a bit more than a year. She was a natural telekinetic with a Soul Gem that gave her telepathic powers as well. She also had detective skills and could pick locks with her mind (thanks to the TK).
Metamorph - I don't really have one of these either, unless you count Fang, who was a reluctant werewolf (and consequently had human and lupine forms). He was an immunologist who accidentally infected himself while trying to discover a cure for lycanthropy. Pretty much a Beast knock-off.
Mystic - My initial thought is to list Amethyst, but as a GMPC, she's as much prop and plot device as actual character. So I'll go with ColdFire. She gained mystical cold powers after being kidnapped and transformed by an ice demon. She's kept a bit of that otherworldly essence, which manifests as a small Magic Pool that's separate from her cold powers.
Patriot/Avatar - I built an NPC named Victor for a villain group; he was an undercover RCMP officer who had infiltrated a mutant liberation supervillain group. I later rebuilt him as a full-blown hero for a high-level hero campaign. He would have been Canada's premier superhero, their answer to Captain America. Alas, the campaign never really took off, and I never got to play him.
Powered Armor - One summer many years ago, my GM had the idea of running an aquatic campaign. My character was a scientist who had perfected a deep-sea exploration supersuit. That was Riptide. He had increased strength, Life Support, a large amount of both swimming and flight, and an electrical EB that was really nasty underwater.
Speedster - Brian Brodeur was a world champion skier who was about to be devoured by a demon, but was rescued and given the chance to work for an extradimensional cabal of well-intentioned but slightly insane entities known as the Pentarchy. Already blessed with phenomenal physical attributes, he eventually gained superhuman speed and agility, as well as flight powers. Oh, and the Pentarchs gave him a really big gun. And thus he became Desperado. Think Northstar with a BFG, and you've got the idea.
Weapon Master - This would have to be Jack Diamond. In addition to his combat and detective skills, he had a Multipower (and later a VPP) full of exotic weapons--many of which were trophies he'd taken from the villains he defeated. His first trophy was a pair of gauntlets he took from Vengeance (our world's villainous version of the Golden Avenger). Vengeance took offense, and became Diamond's archnemesis.