You can't expect to have a good gpu with good fps with a $300 budget.
PCPartPicker part list:
http://pcpartpicker.com/p/1WZUu
Price breakdown by merchant: http://pcpartpicker.com/p/1WZUu/by_merchant/
Benchmarks: http://pcpartpicker.com/p/1WZUu/benchmarks/
CPU: AMD Athlon II X4 750K 3.4GHz Quad-Core Processor ($79.98 @ OutletPC)
Motherboard: ASRock FM2A55M-DGS Micro ATX FM2 Motherboard ($49.99 @ Newegg)
Memory: G.Skill 4GB (2 x 2GB) DDR3-1333 Memory ($37.91 @ NCIX US)
Storage: Western Digital Caviar Blue 250GB 3.5" 7200RPM Internal Hard Drive ($48.95 @ OutletPC)
Video Card: PowerColor Radeon HD 6670 1GB Video Card ($48.98 @ Newegg)
Case: HEC Enterprise MicroATX Mid Tower Case ($9.99 @ Newegg)
Power Supply: Corsair Builder 430W 80 PLUS Bronze Certified ATX12V Power Supply ($19.99 @ Microcenter)
Total: $295.79
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-03 18:00 EST-0500)