I figured as much. What settings do you plan to play at?
I have a Radeon 7950 and on Skyrim at your res, I max it with AA and AF on the highest they can go, so at your budget, a 7850 should do the same, but with settings toned down a bit (still on ultra mind you).
Are you near a microcenter? The reason I ask is because they have a $50 discount on Z77 and Z68 motherboards when you buy an i5-3570k/3770k and i5-2500k/i7-2600k/2700k.