This might work. If you have a little more to play with then upgrading the GPU to GTX660 or R9 270 would be the way to go, whichever you could afford. But it should run your medium settings fine. Keeping an eye out on sales on memory and possibly going for a 970 base mobo, you can easily tweak this under $600.
PCPartPicker part list:
http://pcpartpicker.com/p/2ypAr
Price breakdown by merchant: http://pcpartpicker.com/p/2ypAr/by_merchant/
Benchmarks: http://pcpartpicker.com/p/2ypAr/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ TigerDirect)
Motherboard: Asus M5A99X EVO R2.0 ATX AM3+ Motherboard ($107.99 @ NCIX US)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-2133 Memory ($79.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @ OutletPC)
Video Card: Gigabyte Radeon R7 260X 2GB Video Card ($145.66 @ Newegg)
Case: Corsair 200R ATX Mid Tower Case ($49.99 @ NCIX US)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($49.99 @ NCIX US)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($19.98 @ OutletPC)
Total: $623.57
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-01-09 12:24 EST-0500)