Re: What now?
Okay, here's a suggestion:
Space is divided into four Quadrants. You have the Earth/Terran/Human Empire/Federation/Soviet/Commonwealth/whatever in one quadrant. Two others quadrants are regions colonised by other races or groups of races, and all Empires are of similar size.
The fourth region is currently unexplored. The reason is that FTL travel was range-limited, and the closest system in that quadrant to Known Space is beyond that range. However, a scientific breakthrough has increased this maximum range, and the "Great Void" can be crossed. Once across that gap, ships can refuel (solar power, skim gas giants a la Traveller, or whatever) and continue deeper into the unexplored territory.
All three civilisations know about the breakthrough, and race to complete the first ships to cross the Void (called "Voidships" perhaps to differentiate them from "Starships"?). Perhaps they are mostly engine, with little room for payload (perhaps the breakthrough was simply improving the FTL engine performance sufficiently to carry a minimum payload, a natural progression, hence everyone can do the same thing at roughly the same time).
The borders of Known Space are such that each civilisation borders the Void, but there are only one or two Crosspoints within each civilisation - that is, there are only one or two systems in the Dark Quadrant (do you like the names I'm giving things as I go along ?) close enough to Jump/Warp/FTL to from Known Space. From there, events are up to you...
Options:
1. The ship can be small in payload - just the PCs and their supplies (think Lost in Space but without being lost). Or it can be huge, and the PCs are a key part of the team (think Star Trek). What their exact role is in this latter case depends on what you think the players would prefer - bridge crew, ship's marines, ship's fighter pilots, etc.
2. Relationships between Empires could be friendly, cordial, cool, strained, hostile, or die-you-*&%$s! This attitude may effect reactions when ships from rival Empires arrive over the same piece of Real Estate. Or the rules may change across the Void - and change either way.
3. Assume the PCs are on the first ship to Voidtrek. What will they find? New Life and New Civilisations as they Boldly Go? Will such Life be Friendly, Unfriendly or Pleased To Eat You? Maybe it will be still evolving (Welcome to Jurrasic Planet). Will they instead find shattered Ruins of an ancient civilisation, once proud rulers of the entire Quadrant, with remnants of valuable hi-tech gizmos lying around? Will some vestiges of this civilisation remain in some form?
4. As the campaign progresses, will they need to return to base periodically for supplies, or can they keep going, self-sustained ("Our five-year mission...")? At what rate will new Voidships be built and join the exploration mission? How often will the PCs encounter Voidships from their neighbours? Possible campaign events include rescuing a sister-ship, rescuing a neighbour's Voidship (perhaps from an unfriendly neighbour), or getting in trouble themselves and being rescued by another Voidship (reverse of previous scenarios). Perhaps war breaks out back "Home" and the Earth Empire's Crosspoints are captured by the enemy - the crew must find another way home, perhaps through the "neutral" third Empire. However, since the volume of the Dark Quadrant is known, there is a definite campaign goal - explore and claim as much of it as possible! Other goals may be added as desired ("Hey! According to these hieroglyphs, these long-dead aliens had a Stargate on their home planet, and they used that to leave this galaxy for another! Maybe they're not long-dead after all...").
Anyway, that's my suggested campaign skeleton.
Mantis