I'm sorry but with prebuilts you really are destroying the value of the PC you could have.
First of all, before we can make a part list for this new custom PC, we need some specifics. More specific than "Can run Battlefield 4". Any monkey computer can run it, its just whether it will go faster than 1FPS. So first, how fast do you want it and at what graphics level? If you want the highest premium settings at full speed, you'll have to dish out more for the GPU than your other parts. (other than maybe the CPU)
Ninja edit:
First point five, whats your monitor's max resolution?
Second, quality over bang/buck? This will determine AMD/ATI over Intel/Nvidia.
Third, do you want USB 3.0?
Fourth, is the quietness of the PC important? How important?
the highest settings on nearly any game. Basically I want it to kick ass. Usb 2.0 willmbe fine and it can be as loud as it wants. My monitor res is like 1024 wide by 700 something. But I am planning on getting a bigger one