Not post-apocalyps Sci-fi again!
Take something that isn't sci-fi and if it is do so it isn't an Post-apocalyps one.
LIke, the Earth is still fine but is almost depleted and you are a company that as to thrive.
( and inventuelly capture Earth)
or that you are a colony ship and you can get shipments from Earth.
These have been done before, and in fact more often then Post- apocalyptic. (Besides who said the Earth was destroyed)
I vote for Spaceship: Realistic.
And that doesn't preclude meeting aliens, it just means that you need cryonic tube thingies that freeze you for the thousands of years it would take to get to another solar system at STL speeds.
And then you'd have to be lucky to land on an inhabited world, at which point you must be lucky enough to actually recognise the lifeforms as intelligent, and vice-versa, hope they understand you. Then hope a peace and such is possible. Even setting up contact might take years. For all we know their might be colective intelligences out there, or aliens based on a whole other symptom at us.
Also, the spaceship wasn't intended as a a cryoship(though that can be changed). It was designed as a generation ship. Also, the idea was not about how the humans would rebuild their civilization, but more about the live and such on the spaceship itself, now that it is falling apart due to internal struggle and such.(Though that can be changed)