For speakers in that budget, I would be looking at a Paradigm Premiers 800F and 500C setup. Excellent linearity and good dynamic range. You might also look at an Arendal front-stage; a 1723 front stage would be a knock-out speaker system. If you want very good speakers that aren't quite as expensive, look at some Monoprice Monolith speakers, specifically, the 365c center and the THX-460T towers. I would skip the power sound audio speakers, and I think they are being recommended by people who have never heard them in person. For subs, a dual Hsu VTF-3 mk5 system would be an excellent choice.
Given this is an open room, I would go for a TV over a projector. Light control seems like it would be more difficult in an open room. Although if you can ensure good light control, I would go for a projector, but that means being able to completely shut down all ambient light when you want to watch something.
As for surround channels, that is tricky to do in an open room. Personally, depending on your situation I would just use some in-ceiling speakers for a 5.1 or 7.1 system if you can't get acoustic symmetry in your room.
For a receiver, I would be looking at Denon, Marantz, or Yamaha. Beggers can't be choosers, and the AVR market is pretty barren right now since no one can get any stock. You will just have to grab whatever you can get.
