I would suggest going with an amd processor and an ati gpu.
Processor: AMD bulldozer fx-4 4100 3.6ghz ($100)
Motherboard: A basic motherboard with overclocking features ($100)
Memory: 8gb Corsair Vengeance ($90) Which are enough for gaming (current) and even for multimedia
Hard Drive: 1Tb Western Digital Caviar black 6gb/s ($100)
Power Supply: Corsair CX500 modular 80+ bronze 500W ( not sli/crossfire capable ) ($70)
Graphics card: Msi 7950 3Gb ($250)
Case: This comes down to your liking ($90)
Regarding the processor getting an intel core i5 3570k of 4570k ( most common ) would mean 2.5x the price of the 4100. In terms of raw power intel beats amd by a mile but for everyday use and gaming is enough.
The is no room for an ssd but a 7950 is way much better than a 6670 ( you'll play crisis 3 maxed out @ a resolution of 1920 x 1080 ). Also you will be having a stock cooler which will not give you a lot of overclocking headroom.
If you can squeeze just a $150 more you could get a better cooler and an ssd 120gb ( something around that ) . If you get an ssd you could then go for a 1TB caviar green/blue which is cheaper and you could use if for storage.
Hope this has been of help.
Lukee