I've got a spare Q6600 based system so very similar with an nVidia GTX 670 and it plays games like Far Cry 3, Borderlands 2, Civ 5 on medium to high settings fine at 1080. The mobo is most likely only PCIE v1.0a/1.1 so don't go too crazy on a new card.
Best 2nd hand card in budget you can find would be my choice.
@MisteryAngel @Streetguru I just heard back from him. His dad is willing to spend around $500 (I'm sure there would be some wiggle room, but try to keep it under $500.) It would have to be a full computer (Case, Motherboard, CPU, PSU, GPU, Ram) I can probably use their old hard drive. I have a key for Windows 8.1 Pro, so that is not an issue.
His current power supply is only 350 watts, so I don't think it would support overclocking or a GPU
I'd go with either this or that APU build above if you really want to keep the cost low
PCPartPicker part list: http://pcpartpicker.com/p/ZRvFjX
Price breakdown by merchant: http://pcpartpicker.com/p/ZRvFjX/by_merchant/
CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($68.99 @ NCIX US)
Motherboard: Gigabyte GA-F2A68HM-DS2H Micro ATX FM2+ Motherboard ($46.99 @ SuperBiiz)
Memory: Patriot Signature 8GB (2 x 4GB) DDR3-1600 Memory ($38.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($51.88 @ OutletPC)
Video Card: Gigabyte Radeon R9 380 4GB Video Card ($193.98 @ Newegg)
Case: Fractal Design Core 1000 USB 3.0 MicroATX Mid Tower Case ($33.99 @ SuperBiiz)
Power Supply: Rosewill 600W 80+ Bronze Certified Semi-Modular ATX Power Supply ($64.99 @ Newegg)
Total: $499.81
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-11-18 13:29 EST-0500
Dude! I can't thank you enough! This is an awesome setup! I will let him know and we will start working on this!