Here's what I would do, and no, the i7-3770k is not a good choice for gaming :
PCPartPicker part list:
http://pcpartpicker.com/p/1DsTf
Price breakdown by merchant: http://pcpartpicker.com/p/1DsTf/by_merchant/
Benchmarks: http://pcpartpicker.com/p/1DsTf/benchmarks/
CPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor ($219.98 @ Outlet PC)
CPU Cooler: Corsair H100i 77.0 CFM Liquid CPU Cooler ($89.99 @ NCIX US)
Motherboard: MSI Z77A-G45 Gaming ATX LGA1155 Motherboard ($119.99 @ SuperBiiz)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($57.99 @ Newegg)
Video Card: Sapphire Radeon HD 7950 3GB Video Card ($199.99 @ Newegg)
Case: Antec Eleven Hundred ATX Full Tower Case ($64.99 @ NCIX US)
Total: $752.93
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-09-13 22:01 EDT-0400)