Ok, what I would do is buy it off of iBUYPOWER. Its a good site, I got mine off of there. If your going to buy it, I would buy it NOW, as they're having a labor day sale which ends in 2 days time... I'll give you some basic specs that you would probably want to choose to run BF3 nicely and be within your budget.
Case: Any
Processor: i5-2500k @3.3ghz
Cooling: I like liquid cooling, but if you want only fans, then get one of the more advanced ones (pricier ones, like an extra $20)
RAM: DDR3, get the 8GB as its a free upgrade from the 4GB due to the sale
Graphics: Nvidia GeForce GTX560Ti -1GB superclocked
Free stuff: May as well select it, its FREE!
Motherboard: [SLI] ASUS Sabertooth P67
Power Supply: Thermaltake TR2 TRX-750M Labor Day Special! FREE Upgrade to Thermaltake 850 Watt
Everything else: keep as is...
Total price: $1113
The extra $87 you have should cover shipping hopefully
This is the link for the computer that ive customized and selected parts for:
http://www.ibuypower.com/Store/Game_On_E1_Special
Hope this helps