well all your parts should work fine together, and in your price range i would say an amd 7850 for about $150 would be you best bet... but
what are you using your computer for?
that fx8120 is a good processor but is only going to shine on heavy video transcoding or complicated photoshop editing.
if all you want is to surf the internet, listen to music and game a little bit from time to time i would skip the amd fx and video card route and go with an amd trinity a10-5800k and 8gb of fast 1866mhz ram.http://www.tomshardware.com/reviews/memory-bandwidth-scaling-trinity,3419.html
amd's newer apu called richland is going to release in about a month so the prices of an a10-5800k should start to get competitive, I've personally seen that processor go for $100 although its normal price is $150.
that being said, that A10 cpu has a built in gpu(7660g) and overall when gaming is concerned is better quality and faster than a 360/ps3.