For the most part, this will cover you.
The only issue left will be the GPU. For BF4 you will want something more powerful if you want to play on high-ultra. If this goes over your budget I can bring it down some.
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
CPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor ($189.99 @ Microcenter)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ Outlet PC)
Motherboard: Asus P8Z77-V LK ATX LGA1155 Motherboard ($114.99 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($65.79 @ NCIX US)
Storage: Western Digital Caviar Black 500GB 3.5" 7200RPM Internal Hard Drive ($74.99 @ Newegg)
Video Card: Asus GeForce GTX 660 Ti 2GB Video Card ($299.99 @ Amazon)
Case: Cooler Master HAF 922 (Black) ATX Mid Tower Case ($99.99 @ Newegg)
Power Supply: SeaSonic 620W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($74.99 @ Newegg)
Operating System: Microsoft Windows 8 (OEM) (64-bit) ($79.99 @ Newegg)
Total: $1030.70
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-04-30 17:58 EDT-0400)