$1K is a good budget. I just recently built a system for that much with a 2500K, monitor, and a Radeon 6870. See what can be done here:
CPU+RAM: http://www.newegg.com/Product/ComboDealDetails.aspx?ItemList=Combo.644341
COOLER: http://www.amazon.com/Cooler-Master-Hyper-Sleeve-RR-B10-212P-G1/dp/B002G1YPH0/ref=sr_1_1?ie=UTF8&qid=1305704847&sr=8-1
CASE+MOBO: http://www.newegg.com/Product/ComboDealDetails.aspx?ItemList=Combo.646552
PSU: http://www.newegg.com/Product/Product.aspx?Item=N82E16817139020
GPU: http://secure.newegg.com/Shopping/ShoppingCart.aspx?Submit=view
HDD: http://www.newegg.com/Product/Product.aspx?Item=N82E16822152185
That comes out to under $1020. There are ways to get it under $1K, but these components are nice for jus a bit more. The Radeon 6950 I linked is a reference design version that has a high chance to be unlocked to perform like the Radeon 6970 by simply flashing a BIOS. Guide here:
http://www.overclock.net/amd-ati/923129-hd-6950-810-1250-mhz-shader.html
I already have Windows 7, mine is 32-Bit. However, correct me if I'm wrong, I can use my 32-Bit key with a 64-Bit installation disk. If not, I'll need one, but I should be able to get it fairly cheap from my school store.
That should be the case, but will need to be a clean install. Can't have both running on one key...it's one or the other platform. This might be helpful:
http://www.sevenforums.com/general-discussion/25212-both-32-64-bit-version-one-disk.html