Gaming pc (bf3) fair budget

Its very important to know the resolution of your monitor before anyone can answer your question . Each pixel has to be calculated and then drawn by the computer so if there are more of them your game slows .

In general though a top end graphics card costing about $500 can play BF3 on ultra setting at good frame rates . Just the graphics card !
The build you outline above will play it on settings about equivalent to a console , but not anywhere near ultra settings .
For that you will need to spend much more