Gaming mostly...so I got ya a 6-core FX-6300 and put the budget on a more powerful HD 7870 Ghz Edition. If your budget allows u could keep FX-8320 too but 6 cores should be enough for gaming.
BTW, your list's PSU is not enough for powering up. It should be at least 500W
How about this?
PCPartPicker part list:
http://pcpartpicker.com/p/1kT7C
Price breakdown by merchant: http://pcpartpicker.com/p/1kT7C/by_merchant/
Benchmarks: http://pcpartpicker.com/p/1kT7C/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Newegg)
CPU Cooler: Cooler Master Hyper 212 Plus 76.8 CFM Sleeve Bearing CPU Cooler ($19.99 @ Newegg)
Motherboard: Asus M5A97 R2.0 ATX AM3+ Motherboard ($94.99 @ Microcenter)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($64.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @ Outlet PC)
Video Card: Sapphire Radeon HD 7870 GHz Edition 2GB Video Card ($169.99 @ Newegg)
Case: NZXT Tempest 210 ATX Mid Tower Case ($47.06 @ Amazon)
Power Supply: XFX 650W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($49.99 @ Newegg)
Optical Drive: LG GH24NS95 DVD/CD Writer ($14.94 @ Newegg)
Total: $626.92
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-07-26 11:47 EDT-0400)