I'm rereading Harry Potter for the billionth time and chapter 2 in book 6 is set in Snapes house. So clearly he has a home, but in book 5 where Umbridge is trying to throw out Prof. Trelawny, she says "But where will I go? Hogwarts is my home!" which strongly insinuates that she lives there permanently and has no house of her own.
Hagrid obviously lives there as he's the gamekeeper. But what about everyone else? Do you think they're given the choice when they get a job whether they live there full time or not?
And where do they sleep? Do they have sleeping quarters somewhere? I notice it's never really mentioned in the books about where the teachers sleep. It must be a bit miserable, living in your place of work, even if it is a magical castle.