Avoid the bulldozer quad-core. As much as I'm an AMD fan, this generation of AMD processors isn't very good.
(the 4100series performs lower than the previous generation Phenom quad-cores).
ASUS P8Z77-V lk - $138.55
Intel i3 Dual Core - $142.60
Corsair Vengeance 1600Mhz 2x4GB RAM - $60.91
Coolermaster Hyper 212 Heatsink - $30.98
XFX Radeon HD 7870 Double D - $299.99
Corsair TX650M 650W Powersupply - $104.99
Crucial M4 128Gb SSD - $121.99
Bitfenix Shinobi - $69.99
Total: $970.00 before tax and shipping, AFTER MIR.
This is a NON-overclocking build, as the processor is not unlocked, and the motherboard doesn't have the necessary VRM heatsinks to handle increased voltage. I used an i3 dual core since benchmarks show that framerates will remain similar from the i3 to the i7 processors. You want to focus mainly on video card.
I replaced your 1TB harddrive with a 120GB SSD. 120GB SSD should be enough for a Windows install and up to 6 large games installed simultaneously. You'll have to purchase a second HDD for media storage purposes a little later when you have more money saved up.
The only current generation (28nm) video cards at the $300 mark are currently the AMD 7800 series. Which is unfortunate, because they're a little overpriced for the performance they give you. However, the next level of video cards (GTX670, 7950) are in the $400+ range. If you wait a couple of weeks, Nvidia may release their GTX660 which
should drive down the price of the 7870.