I would preffer this build!
PCPartPicker part list:
http://pcpartpicker.com/p/QsqQcf
Price breakdown by merchant: http://pcpartpicker.com/p/QsqQcf/by_merchant/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($119.99 @ Newegg)
CPU Cooler: Cooler Master Hyper N520 43.8 CFM Sleeve Bearing CPU Cooler ($39.99 @ Newegg)
Motherboard: Gigabyte GA-970A-D3 ATX AM3+ Motherboard ($97.27 @ TigerDirect)
Memory: Kingston Fury Black Series 8GB (2 x 4GB) DDR3-1333 Memory ($79.99 @ NCIX US)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($54.98 @ OutletPC)
Video Card: MSI Radeon R9 270X 2GB TWIN FROZR Video Card ($184.98 @ SuperBiiz)
Case: Cooler Master N600 Windowed ATX Mid Tower Case ($69.99 @ Newegg)
Power Supply: Corsair Gaming 600W 80+ Bronze Certified ATX Power Supply ($69.99 @ Micro Center)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($26.97 @ Newegg)
Operating System: Microsoft Windows 8.1 - 64-bit (OEM) (64-bit) ($95.98 @ OutletPC)
Total: $822.13
Prices include shipping, taxes, and discounts when available
You must get a cheaper CPU to get a better GPU the AMD Fx-6300 runs awesome withou any problem! So at your budget I prefer you must get the AMD FX-6300 and a MSI Radeon R9 270x 2Gb it will run games like Call Of Duty and Battlefield on ULTRA you will get a average FPS at 35-40+