PCPartPicker part list:
http://pcpartpicker.com/p/X7pKxr
Price breakdown by merchant: http://pcpartpicker.com/p/X7pKxr/by_merchant/
CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($69.98 @ OutletPC)
Motherboard: Asus A78M-E Micro ATX FM2+ Motherboard ($34.99 @ Newegg)
Memory: Team Dark Series 8GB (2 x 4GB) DDR3-1600 Memory ($57.99 @ Newegg)
Storage: Western Digital RE3 1TB 3.5" 7200RPM Internal Hard Drive ($48.00 @ Amazon)
Video Card: Sapphire Radeon R9 280 3GB Dual-X Video Card ($164.99 @ Newegg)
Case: Rosewill FBM-01 MicroATX Mini Tower Case ($23.99 @ Amazon)
Power Supply: EVGA 430W 80+ Certified ATX Power Supply ($18.99 @ NCIX US)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($88.98 @ OutletPC)
Total: $507.91
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-12-21 20:46 EST-0500
This build should do just about everything you want it to.
Go with a 500Gb hard drive, and you're below your price point. Also, if you're feeling adventurous, you can find legitimate copies of windows (with real COA) on ebay for around $60. Obviously you would have to be skeptical and careful (and I wouldn't necessarily recommend it), but it's an option if you are on an extreme budget.