Start Here:
Top 10 Home Theater Projectors
I have owned several of these projectors. Everything depends on your situation. In a completely light controlled room I highly recommend the Epson 5030ub (e - wireless hdmi) and the Panny PT-AE8000. Both are amazing 1080p projectors. The 5030UB has good 3d as well, but no projectors have great 3D unless you get 2 of them and do a really good passive setup.
I will be very blunt about this. Anything over $3,000 right now is almost zero gain in light controlled room. The only reason you would step above this is to become an early 4k adopter. That is outside of your listed price range. The Sony 4k projectors are amazing, but still very expensive and there is no major content. I had the same decision to make and decided to keep the 5030ub instead of going 4k right now.
LED projectors are still lacking as well.