$650 with everything is a very tight budget. This is what I came up with:
PCPartPicker part list:
http://pcpartpicker.com/p/3C9si
Price breakdown by merchant: http://pcpartpicker.com/p/3C9si/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3C9si/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Newegg)
Motherboard: Asus M5A78L-M LX PLUS Micro ATX AM3+ Motherboard ($44.99 @ Micro Center)
Memory: A-Data XPG V1.0 4GB (1 x 4GB) DDR3-1600 Memory ($34.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: EVGA GeForce GTX 750 1GB Video Card ($115.99 @ NCIX US)
Case: Sentey CS1-1398 PLUS ATX Mid Tower Case ($19.00 @ Newegg)
Power Supply: Corsair Builder 430W 80+ Bronze Certified ATX Power Supply ($34.99 @ Micro Center)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($19.98 @ OutletPC)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($89.99 @ NCIX US)
Monitor: Acer V226HQLAbd 60Hz 21.5" Monitor ($106.93 @ NCIX US)
Keyboard: Logitech K360 Wireless Mini Keyboard ($22.07 @ B&H)
Mouse: Zalman ZM-M200 Wired Optical Mouse ($9.48 @ SuperBiiz)
Total: $658.39
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-05-01 18:05 EDT-0400)
It won't be able to play every game on max settings. I'd say medium-max depending on the game. If you could give us an extra $150 to work with then things will get much better.