First off, I'm no expert, so hopefully others will chime in...
You'll probably want an AVR that does bi-amping since those will handle up to 250w RMS (according to Crutchfield, anyway). Other than that, figure out what will meet your needs.
For $300, you'll probably need to look at a refurb or used. I say that b/c you want 7.1 + you'll probably need more than your standard watts/per channel to push the BA's to their potential. You might look for a good used 9.2 AVR w/ 100-110 watts per channel @ 8ohms. Onkyo, Denon, and Yahama seem to be the frontrunners around here.
You'll probably want an AVR that does bi-amping since those will handle up to 250w RMS (according to Crutchfield, anyway). Other than that, figure out what will meet your needs.
For $300, you'll probably need to look at a refurb or used. I say that b/c you want 7.1 + you'll probably need more than your standard watts/per channel to push the BA's to their potential. You might look for a good used 9.2 AVR w/ 100-110 watts per channel @ 8ohms. Onkyo, Denon, and Yahama seem to be the frontrunners around here.