I don't care for Zombies, but here is my two cents:
Why would you want 1000 people on board? No, no, no. Get 100-120 people that you like or want on your ship
There are multiple reasons. More people means you can do more things at once, or do things in more areas at once. It also means you don't have as large of a risk at yet another genetic bottleneck (Humans have less genetic diversity across the entire population than any other primate, much less any other globally distributed species).