The optimum core parts, for Battlefield 3, might be:
CPU: i5-3570K
Cooler: Coolermaster Hyper 212Evo
Mobo: Asus P8Z77-V LK (ASRock Z77 Extreme4 is a budget option)
GPU: nVidia 660Ti (or GTX 670 if Budget will stretch)
PSU: XFX 550w
Add decent mid-towerATX case, hard and optical drive, and that will happily play BF3 at Ultra @ 1080p
Add a 128Gb SSD, if you want, something like Samsung 830, or Crucial M4 (nice to have but nothing like essential)
If you don't want to overclock, and don't plan on adding 2nd graphics card, in future:
Change CPU to i5-3450, and mobo to any Asus H77 (rather than Z77)