I've got the HD700X and it's very good, had it up to 110" in a large-ish room before and it still looked very good. Probably don't quite need 1080p for that sort of size unless you're sat very close to the screen.
HD700X should also fit right in your budget, though I bought mine a year ago so newer versions are probably out, the 600X as suggested looks like it's probably the newer version of the 700X and still in your budget.