Here is everything, all parts included, with a little bit of room in your budget for some minor tweaks:
CPU:
Intel Core i5-2500K for $225 Standard top end gaming CPU.
Motherboard:
A$US P8P67 PRO for $175 Full featured board, capable of cross fire, plenty of overclocking utilities.
Video:
HIS H695F2G2M Radeon HD 6950 2GB for $245 after rebate Unlock this to a 6970, and you can add a second card for an upgrade.
RAM:
G.SKILL Value Series 8GB for $80. Standard issue, nice voltage.
HDD:
SAMSUNG Spinpoint F3 HD103SJ 1TB for $65.
Heat Sink:
COOLER MASTER Hyper 212 Plus for $42. Overclocking is so easy with the sandybridge, and this inexpensive cooler will keep your temps in line.
DVD:
LG Black 24X DVD for $25
Case:
COOLER MASTER HAF 922 for $90 after rebate Plenty of room for a comfortable build. This case has lots of nice features for cable management, good air flow, cut out for replacing cooler, etc. Cases are personal choices, so if this does not appeal, there are plenty of other selections.
Power Supply:
XFX Core Edition PRO850W for $116 after rebate
8 Pin Extension:
APEVIA 9 1/2" Cable for $7. Need this with bottom mount power supply cases to reach the supplemental motherboard power. Just makes the build a little easier.
OS:
Microsoft Windows 7 Home Premium 64-bit for $100.
Monitor:
ASUS VH236H Black 23" 2ms for $169 after rebate. Top ratings from Newegg on this model. Decent size, 2 ms response. Includes speakers, but you may want to purchase them separately.
Mouse:
Logitech MX 518 8 Buttons for $36. Highly rated gaming mouse.
Keyboard:
Saitek Cyborg V5 for $46. Not only hihgly rated, but it looks cool too.
Total price: $1421 shipped to your door, ready to build.
You did not indicate your experience at building out PCs - need references?
Edited to correct Asus hyperlink.