Listen to speakers to decide on the ones you want. Your choice of speakers will dictate if a receiver will suffice or if you will need an external amplifier. Your room isn't all that large, but if you choose speakers that present difficult loads to power you'll want an external amp.
Depending on your room layout you may or may not want to go with subwoofer(s). You get more for your money going with internet direct brands HSU, Outlaw, Rhythmik, Epik.
Denon, Marantz, Yamaha all make good higerh end receivers, many have pre outs and so can act as a preamp. Onkyo's are known for running very hot, and lately have had reliability issues. I own one, but I don't know if I'd recommend them now.
NAD and Rotel are brands that don't compete on features but you may find you like them, and if you're not about getting the latest surround sound standards they might work for you. Anthem in another higher end company that you may want to look at.
I think all the above make separates if you decide to go that route. Outlaw and Emotiva a respected internet direct brand amplifiers. Amplifier Technologies is a good made in the USA amp company that oems amps for other companies.
B & W 800's I think list for well outside your budget, and I think they're pretty big. You mention a living room, not a purpose specific room. Make sure you pick speakers that can be properly placed in your room. As others have mentioned room treatments will help you get the best sounding room, but aren't always easy to incorporate into a living room.