Good Intel Based Gaming PC that is about $600.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i3-4130 3.4GHz Dual-Core Processor ($119.97 @ OutletPC)
Motherboard: Gigabyte GA-B85M-D2V Micro ATX LGA1150 Motherboard ($57.79 @ Amazon)
Memory: A-Data XPG V1.0 8GB (2 x 4GB) DDR3-1600 Memory ($64.99 @ NCIX US)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($54.43 @ OutletPC)
Video Card: PowerColor Radeon HD 7870 GHz Edition 2GB Video Card ($139.99 @ Newegg)
Case: NZXT Source 210 (Black) ATX Mid Tower Case ($32.99 @ Micro Center)
Power Supply: SeaSonic S12II 520W 80+ Bronze Certified ATX Power Supply ($59.99 @ Amazon)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($14.99 @ NCIX US)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($89.98 @ OutletPC)
Total: $635.12
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-05-10 02:42 EDT-0400)

I think something like this would work, but do you need os, and are you going to be recording games?
 
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