Here's what I recommend. It will perform a lot better than the PS4 and the Xbox One, without a single doubt :
PCPartPicker part list:
http://pcpartpicker.com/p/3fQ4e
Price breakdown by merchant: http://pcpartpicker.com/p/3fQ4e/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3fQ4e/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Amazon)
Motherboard: Asus M5A97 LE R2.0 ATX AM3+ Motherboard ($74.97 @ OutletPC)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($64.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($57.98 @ OutletPC)
Video Card: Sapphire Radeon R9 270 2GB Video Card ($189.99 @ Newegg)
Case: Cougar Solution (Black) ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: Corsair Builder 500W 80+ Bronze Certified ATX Power Supply ($39.99 @ Newegg)
Total: $577.90
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-24 19:48 EDT-0400)