Thats not an ideal gaming machine budget, but we can get something close. $800-$900 would get you several orders of magnitude faster performance, but in that price range, this is what I would build.
Motherboard: Asus Socket 1155 P8H67-m
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131711 $114
Processor: Intel socket 1155 2.93 Ghz Quad core
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115089 $189
Ram: Corsair 4GB (2X 2gb) DDR3 ram kit
http://www.newegg.com/Product/Product.aspx?Item=N82E16820145339 $29 (buy a second kit later when funds permit)
Power supply: Antec 650 watt psu
http://www.newegg.com/Product/Product.aspx?Item=N82E16817371044 $59
Hard drive: Western Digital 500GB SATA 7200 RPM
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136769 $39
Optical drive: samsung 24x DVD burner
http://www.newegg.com/Product/Product.aspx?Item=N82E16827151233 $17
Case: Cooler Master CM690 II advanced
http://www.newegg.com/Product/Product.aspx?Item=N82E16811119216 $89
Video card: Gigabyte 260 GTX
http://www.newegg.com/Product/Product.aspx?Item=N82E16814125391 $99
So thats $635 for the hardware alone.
Operating system if you need a license and don't have access to an educational discount
http://www.newegg.com/Product/Product.aspx?Item=N82E16832116992 $134
That puts you right at: $769
If you need to cut corners, there really isn't that much to cut. you could go with a slower duel core processor for around $90. Going with a smaller hard drive doesn't really get you any major savings ($1-$4 dollars at most). You could go with a cheaper case, but seeing as the case is the single component you will have the longest out of any of your computer parts, I wouldn't. Thats not a top of the line video card by any means, but its about the best price vs performance ratio you are going to see for a while. A 460 GTX is going to start at $200ish. Power supply, you need a minimum of a 550 watt anyways with that card, may as well build in a little upgrade budget for $10 more.
That doesn't include monitor, keyboard, etc too, so you may need to budget for those as well.