Around $200 under your budget. If you want to, you could probably upgrade to a 4770K instead, but I dont see much point if all you're doing is gaming.
CPU: Best intel i5 out there. Great for gaming.
Cooler: Pretty much the standard by now, great overclocking potential and runs really quiet.
MOBO: Good-Great overclocking, fairly cheap. Loaded with features.
RAM: It's a combo with the barracuda, but it's really fast.
HDD: Seagate Barracuda 64MB cache 7200rpm, best hard drive price-performance, much cheaper than WD but just as good,
SDD: Really nice SSD, use it to store your OS and such. Very fast, but if you want more speed consider the Kingston HyperX 3K instead.
Video Card: Tek Synd have a video about this, great card. Once you get it ramp the memory clock up as high as it allows as long as it stays below 70-80 degrees.
or: If you wanna save money, you can get a HD 7970 instead as it is essentially the exact same thing, but the 280x has like a 3fps boost, if you are gonna go with the 7970 get the ASUS DCII, tek synd also have a vid on this.
Case: Silent with great airflow, also has a window to show off.
Power Supply: Some would say that this is overkill, but considering the 280x draws almost 400w when using furmark, I included this in case. Also it's semi-modular and has the same capacitors as a SeaSonic.
Optical Drive: The cheapest one.
OS: Get Win8, please. It has a performance boost of approx. ~2-3 in most games and is snappier. If you do I advise you get StartIsBack and check out teksynd's vid on it.
Headset: Has a microphone and 7.1 HD surround sound. Logitech make great products.