since you didn't write a budget i could probably give you 2 build INTEL and AMD idk what you like and you can choose BOTH run BF3 SMOOTHLY so don't worry
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Build 1:- INTEL
CPU: Intel Pentium G860 3.0GHz Dual-Core Processor ($68.99 @ Mac Mall)
Motherboard: ASRock H61M-DGS Micro ATX LGA1155 Motherboard ($44.99 @ Amazon)
Memory: Patriot Viper 3 8GB (2 x 4GB) DDR3-1600 Memory ($25.99 @ Newegg)
Storage: Hitachi Deskstar 1TB 3.5" 7200RPM Internal Hard Drive ($69.99 @ Newegg)
Video Card: MSI GeForce GTX 660 2GB Video Card ($209.98 @ NCIX US)
Case: Rosewill REDBONE ATX Mid Tower Case ($34.99 @ Newegg)
Power Supply: Antec 450W ATX12V Power Supply ($35.83 @ NCIX US)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($15.99 @ Newegg)
Total: $506.75
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Build 2:- INTEL (with core i3) why core i3? because in the pc above you WILL LAGG in BF3 Multiplayer in 64MAN MULTIPLAYER MATCHES
CPU Intel Core i3-2100 3.1GHz Dual-Core Processor $109.99
Motherboard ASRock B75M Micro ATX LGA1155 Motherboard $64.99
Memory Patriot Viper 3 8GB (2 x 4GB) DDR3-1600 Memory $38.99
Video Card MSI GeForce GTX 660 2GB Video Card $239.98
Case Rosewill REDBONE ATX Mid Tower Case $34.99
Power Supply Antec Basiq 500W ATX12V Power Supply $48.99
Optical Drive Lite-On iHAS124-04 DVD/CD Writer $15.99
(nothing much changed in this build i just threw in an upgraded PSU (450 to 500)
so you can Overclock. and i changed the CPU to an i3 and the mobo to a B75.
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AMD:-
CPU Intel Core i5-2300 2.8GHz Quad-Core Processor $179.99
Motherboard ASRock H61M-DGS Micro ATX LGA1155 Motherboard $39.99
Memory Pareema 8GB (2 x 4GB) DDR3-1333 Memory $31.89
Storage Seagate Barracuda 500GB 3.5" 7200RPM Internal Hard Drive $54.99
Video Card Sapphire Radeon HD 7950 3GB Video Card $304.99
Power Supply Corsair Builder 430W 80 PLUS Certified ATX12V Power Supply
PS
in the AMD build you still need a case and an optical drive the total would be just above 670~)
ALL OF THOSE are capable of running BF3 on high/ultra smoothly but the first build would lagg in ONLY AND ONLY 64 MAN MULTIPLAYER MATCHES that means it wouldn't lagg if the match had 32
Well,Enjoy