Do you need Windows, Monitor, Keyboard, Mouse?

If you're going to obtain Windows on your own:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor ($199.99 @ Newegg)
Motherboard: ASRock H81M-HDS Micro ATX LGA1150 Motherboard ($58.97 @ Newegg)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($68.00 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($64.99 @ Newegg)
Video Card: Gigabyte Radeon R9 280X 3GB Video Card ($305.91 @ Newegg)
Case: Xion XON-560 MicroATX Mini Tower Case ($44.98 @ Newegg)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($46.24 @ Amazon)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($17.99 @ Newegg)
Total: $802.07
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-27 00:20 EST-0500)

If you need to buy Windows then:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor ($199.99 @ Newegg)
Motherboard: ASRock H81M-HDS Micro ATX LGA1150 Motherboard ($58.97 @ Newegg)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($68.00 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($64.99 @ Newegg)
Video Card: Gigabyte Radeon R9 270X 2GB Video Card ($199.99 @ Amazon)
Case: Xion XON-560 MicroATX Mini Tower Case ($44.98 @ Newegg)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($46.24 @ Amazon)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($17.99 @ Newegg)
Operating System: Microsoft Windows 8.1 - OEM (64-bit) ($99.99 @ Newegg)
Total: $796.14
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-27 00:20 EST-0500)

The first build will run BF4 on Ultra w/ 60 FPS fairly easily at 1920x1080, the second build should be able to hit 60 FPS with a mix of High/Ultra at 1920x1080.