(Nitpick incoming) An assault rifle will be out of your price range, as M16s tend to go for about $15,000. An AR-15, which is semi-auto only (thus not an assault rifle), will be in your price range, and not have so much paperwork with the ATF involved.
If you want a "duty rifle," I'd suggest looking at Colt, LMT, BCM and a few others.
If you want a rifle for the range, and don't require mil-spec or above components, there are a lot of manufacturers that will work nicely.
If you desire a hunting rifle, that will change things a bit.
If you want a target rifle, that's going to look very different from the common 16in carbines.