SAMSUNG T220 Rose-Black 22" 2ms GTG Touch of Color series Widescreen LCD Monitor 300 cd/m2 DC 20,000:1 - Retail - $259.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16824001273
According to Anandtech's LCD buying guide, this is one of the better gaming monitors on the market. Rather expensive compared to a few other offerings, whether or not it's worth the extra money is your choice.
ASUS M4A78T-E AM3 AMD 790GX HDMI ATX AMD Motherboard - Retail - $139.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131366
AM3 mobo with DDR3, great budget board. Would have gone with a GIGABYTE, but reviews said that because of the placement of the PCI-E 2.0 slots, CrossFire would be a tight fit, if even possible. This board has good slot placement, making CF a valid upgrade path. SB750 is AMD's latest southbridge, and the best option for overclocking.
AMD Phenom II X3 720 2.8GHz 3 x 512KB L2 Cache 6MB L3 Cache Socket AM3 95W Triple-Core Black Processor - Retail - $139.00
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103649
Very good gaming processor, comes close to the E8400 on newly formatted systems, but it's strength lies in it's third core, being able to offload any background apps onto it and leaving two just for gaming. Also overclocks very well.
SAPPHIRE 100259-1GL Radeon HD 4870 1GB 256-bit GDDR5 PCI Express 2.0 x16 HDCP Ready CrossFire Supported Video Card - Retail - $189.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16814102801
Great video card, will max out anything at 1680x1050
G.SKILL 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10666) Dual Channel Kit Desktop Memory - Retail - $64.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231200
Decent clock speed, good timings at low voltage. According to the Tomshardware article, 1333 CL7 is one of the best combinations for gaming.
Antec 300 + Antec EA650 650w PSU combo - Combo Price: $106.94
http://www.newegg.com/Product/ComboDealDetails.aspx?ItemList=Combo.198951
Great budget case, quite roomy, and good savings with the combo deal on a good quality PSU.
Logitech G11 Silver & Black 104 Normal Keys 29 Function Keys USB Standard Gaming Keyboard - Retail - $58.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16823126009
Great gaming keyboard, many features.
Logitech MX518 8 Buttons 1 x Wheel USB Wired Optical 1800 dpi Gaming-Grade Mouse - Retail - $39.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16826104178
Comfortable mouse, adjustable DPI switches, good value.
Total: $999.88 before $60 mail-in-rebates.
This build doesn't have a set of speakers, not sure if that's something you want. If it is, you could downgrade your monitor to a more budget-orientated one, get a cheaper keyboard/mouse, or use the $60 from the mail-in-rebates.
Good luck!