I would've done something like this for a gaming PC.
If it *must* strictly be <=$600, then at least a 2gb 7850 or a GTX660.
PCPartPicker part list:
http://pcpartpicker.com/p/G6db
Price breakdown by merchant: http://pcpartpicker.com/p/G6db/by_merchant/
Benchmarks: http://pcpartpicker.com/p/G6db/benchmarks/
CPU: Intel Core i3-3220 3.3GHz Dual-Core Processor ($122.98 @ SuperBiiz)
Motherboard: ASRock H77M Micro ATX LGA1155 Motherboard ($69.99 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($47.98 @ Amazon)
Storage: Seagate Barracuda 500GB 3.5" 7200RPM Internal Hard Drive ($59.73 @ Compuvest)
Video Card: HIS Radeon HD 7870 2GB Video Card ($219.99 @ Amazon)
Case: NZXT Source 210 (White) ATX Mid Tower Case ($29.99 @ Newegg)
Power Supply: Antec 450W ATX12V Power Supply ($38.24 @ Amazon)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($18.98 @ Outlet PC)
Total: $607.88
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-02-26 07:17 EST-0500)