Right, I'll go through the main parts:
CPU: i5 3570K, I wouldn't waste money on an i7 for gaming as you're only paying for the i7's Hyperthreading technology mostly and there's a virtually 0% difference in gaming between the i5 3570K and the i7 3770K, Just get the i5 and over clock it.
One here:
http://www.newegg.com/Product/Product.aspx?Item=N82E16819116504
Motherboard: For gaming I would reccomend the Sabertooth range from Asus, the Asrock Maximus from Asrock. They seem like popular gaming boards and have adequate PCie slots and what not. Just a hint though, I recommend a Z77 for an i5 CPU. NOTE: some of those motherboards are for AMD, be careful!
Here's some gaming motherboard reviews:
http://www.techradar.com/news/computing-components/motherboards/best-motherboard-14-reviewed-and-rated-904229
RAM, HDD and SSD: For gaming I would recmmend at least 8 GB of RAM, or 16GB is even better. Corsair Vengance seems to be the trusted brand for gaming RAM. Here's 8GB but you could buy 2 for 16GB:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820233309
I would recommend at least 1TB HDD for all the gaming storage:http://www.newegg.com/Product/Product.aspx?Item=N82E16822136798 and an SSD (Solid State Drive) for speeding up loading times for example, of at least 124 GB, here:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820227726
Graphics Card: For a fairly high budget of yours I'd recommend an AMD HD 7850 or a Nvidia Geforce GTX 670. They're excellent cards, but not too expensive. Just make sure the're compatible with your Motherboard Here's the AMD:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150609
The Nvidia:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130809
PSU: For powering the hardware there you will need at least a 500W PSU, but I'd recommend 600 or 700W PSU. Just to give you some headroom for upgrades and whatnot. Cooler Master, Corsair and OCZ are good brands. Also, look for an 80 PLUS certificate for efficiency. Here's 600W:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817171036
Here's 700W:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817171037
And that's pretty much it for core parts.
The build here comes to $1080, but you could cut down on some parts such as a smaller SSD, 8GB of RAM or a cheaper motherboard than $220.
There are others such as CD drive, case, cooling to think about aswell, but they are more personal.
Regards,
Dan.