here it is a little over your budget but it should work for you
PCPartPicker part list:
http://pcpartpicker.com/p/3a7Yy
Price breakdown by merchant: http://pcpartpicker.com/p/3a7Yy/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3a7Yy/benchmarks/
CPU: AMD Athlon X4 760K 3.8GHz Quad-Core Processor ($84.74 @ Amazon)
Motherboard: MSI A88XM-E45 Micro ATX FM2+ Motherboard ($62.99 @ Newegg)
Video Card: XFX Radeon R7 260X 2GB Video Card ($135.98 @ SuperBiiz)
Case: Xigmatek Recon ATX Mid Tower Case ($29.99 @ Newegg)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($59.99 @ NCIX US)
Total: $373.69
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-15 03:22 EDT-0400)
here is some benchmarks of the card...
http://techreport.com/review/25473/amd-radeon-r7-260x-graphics-card-reviewed/4
also just put your ram and hdd in the build with your hard drive and you will need to reinstall windows as well
also no matter what you will most likely need a new psu as oem psu are usually on 300w or less. that is why i included one