For slightly over your budget you could get an overclocking set.
PCPartPicker part list:
http://pcpartpicker.com/p/1a9ds
Price breakdown by merchant: http://pcpartpicker.com/p/1a9ds/by_merchant/
Benchmarks: http://pcpartpicker.com/p/1a9ds/benchmarks/
CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor ($227.99 @ NCIX US)
Motherboard: Asus Z87-A ATX LGA1150 Motherboard ($129.99 @ NCIX US)
Memory: Kingston Black 8GB (2 x 4GB) DDR3-1600 Memory ($64.99 @ Amazon)
Total: $422.97
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-27 04:06 EDT-0400)
For your budget, you could get a non-overclocking Xeon 1230v3, which has almost identical performance to the i7 4770.
PCPartPicker part list:
http://pcpartpicker.com/p/3hfZh
Price breakdown by merchant: http://pcpartpicker.com/p/3hfZh/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3hfZh/benchmarks/
CPU: Intel Xeon E3-1230 V3 3.3GHz Quad-Core Processor ($244.68 @ SuperBiiz)
Motherboard: ASRock H87 Pro4 ATX LGA1150 Motherboard ($91.48 @ Newegg)
Memory: Kingston Black 8GB (2 x 4GB) DDR3-1600 Memory ($64.99 @ Amazon)
Total: $401.15
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-27 04:07 EDT-0400)
If you don't want to saturate your budget, here's a non-overclocking alternative too. Slightly slower than the 4670.
PCPartPicker part list:
http://pcpartpicker.com/p/1lVWl
Price breakdown by merchant: http://pcpartpicker.com/p/1lVWl/by_merchant/
Benchmarks: http://pcpartpicker.com/p/1lVWl/benchmarks/
CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor ($189.98 @ SuperBiiz)
Motherboard: ASRock H87 Pro4 ATX LGA1150 Motherboard ($91.48 @ Newegg)
Memory: Kingston Black 8GB (2 x 4GB) DDR3-1600 Memory ($64.99 @ Amazon)
Total: $346.45
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-27 04:09 EDT-0400)
Their gaming performance goes in order. I'd take the 4670k preferably, and maybe overclock it further down the line. If not, then the Xeon wouldn't be a bad choice. Neither would the 4570 by any stretch of the imagination.