Scrap overclocking, at this price point event an overclocked 6300 will not make a 7770 beat a 7850.
PCPartPicker part list:
http://pcpartpicker.com/p/2nHBC
Price breakdown by merchant: http://pcpartpicker.com/p/2nHBC/by_merchant/
Benchmarks: http://pcpartpicker.com/p/2nHBC/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Amazon)
Motherboard: Gigabyte GA-78LMT-USB3 Micro ATX AM3+ Motherboard ($44.99 @ Microcenter)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @ OutletPC)
Video Card: XFX Radeon HD 7850 1GB Video Card ($129.99 @ Newegg)
Case: Antec One ATX Mid Tower Case ($29.99 @ NCIX US)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($59.99 @ NCIX US)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($19.98 @ OutletPC)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($88.98 @ OutletPC)
Total: $543.89
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-12-21 08:00 EST-0500)