Budget: $700
Goal: high-ultra 1080p 60fps settings Battlefield 4
GPU: Radeon R9 280 - $250 (for $50 more can get a R9 280x which out performs a nVidia 770GTX, if you want a $250 nVidia card can get a GTX 760 which under performs the R9 280 marginally)
CPU: Real Budget i3-4130 - $120 (has hyper threading, can play Skyrim at average 74 FPS benchmarked, Far Cry 3 at 84 FPS) for garuanteed top end performance that can run anything on ultra can go with i5-4690k for $230.
RAM: G Skill RibJaw 8 GB DDR3 2133 - $80
Hard Drive: Western Digital 1 TB Blue - $90
Motherboard: Asus H61-M - $50, can even utilize 2133 HZ RAM
Power Supply: Can find many around 600-700w for $50-$70 or so
Case: Can pick a mid tower for around $50 or so
Total: $690 with R9 280 or GTX 760 and i3-4130
$870 with i5-4690k and R9 280X
if you want more future proofing, I would SERIOUSLY highly recommend a different motherboard. That motherboard will get you by for now, but has little to no room for expansion or improvements down the road. you should be good on the processors and video cards for the next few years for the simple fact the processors are pretty new and who knows what the fukk is going on the GPU world right now.. That i3 is crushing the budget gaming buildings right now. Even the $690 build can play any game on high to max settings at around 60 fps right now.