You will probably want an AMD 8-core and at least 8GB of RAM and a video card with at least 3GB. This setup will be the specs for the recommended requirements for battlefield 4 - so you should have no problem running it very smoothly
PCPartPicker part list:
http://pcpartpicker.com/p/1MSsw
Price breakdown by merchant: http://pcpartpicker.com/p/1MSsw/by_merchant/
Benchmarks: http://pcpartpicker.com/p/1MSsw/benchmarks/
CPU: AMD FX-8320 3.5GHz 8-Core Processor ($153.61 @ Amazon)
CPU Cooler: Zalman CNPS9700 LED Ball Bearing CPU Cooler ($39.99 @ Microcenter)
Motherboard: Asus M5A97 LE R2.0 ATX AM3+ Motherboard ($64.99 @ Newegg)
Memory: Mushkin Blackline 8GB (2 x 4GB) DDR3-1600 Memory ($62.99 @ NCIX US)
Storage: Toshiba 500GB 3.5" 7200RPM Internal Hard Drive ($47.50 @ Outlet PC)
Video Card: MSI Radeon HD 7950 3GB Video Card ($179.99 @ Newegg)
Case: BitFenix Ghost (Black) ATX Mid Tower Case ($69.99 @ NCIX US)
Power Supply: Thermaltake SMART 550W 80 PLUS Bronze Certified ATX12V Power Supply ($48.00 @ Newegg)
Operating System: Microsoft Windows 8 (OEM) (64-bit) ($94.98 @ Outlet PC)
Monitor: Gateway FHX2303LAbd 60Hz 23.0" Monitor ($99.99 @ Newegg)
Total: $862.03
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-10-09 19:11 EDT-0400)
Building new systems I usually recommend getting an SSD for longevity and performance. Since hard drives are mechanical they are guaranteed to fail in the future (time can be anywhere from 1 year to 5 years+).