Uncle Jimbo's Bug Huntin' Range
The heroes work to reestablish starfaring civilisation and work out a new, fairer form of society (or to loot and pillage the pathetic do-gooders).
I'd probably make each system more or less self-sufficient, with a few regional alliances and trade pacts.
The campaign might start in a cluster of systems that were once considered a backwater of the Galactic Empire, and thus didn't see much serious fighting until the Human defences were already broken and the Just arrived for their final purge. It could be more interesting, though, to start in a place full of history and peril, with an archaeological expedition to a major capital world. Could this be the fearsome and legendary planet Earth?
Nobody can really say how long since Humanity fell. Apart from anything else the collapse was a Galaxy-wide war that lasted for at least hundreds of years, and many records were lost with the Human capitals.
There are ruins everywhere, some of them planet-sized. A lot of them were zero-bombed or hit with other strategic weapons. Those that are more intact might have war-droids and other dangers.
I think this concept would work OK with a single strong plot that leaves the precise arrangement of worlds and alien species more or less vague. It seems to me that decaying wonders and sinister mysteries are more important to this campaign than demographics.