You will get many ATI/AMD suggestions from this forum. As a counterpoint, here is a list I made up for a previous poster:
A Intel/Nvidia build for value gaming at 1920 x 1080.
1) The Graphics card is the most important factor in most games, particularly at 1920x1080 or larger resolutions.
To that end I suggest a GTX460 as the graphics card of choice. The basic card is a $200 part, and the 1gb card will be about $220.
Launch menchmarks show that it is faster than the $200 ATI 5830. The GTX460 is not quite as fast as the $300 5850, and considerably faster than the $150 5770. According to tom's best graphics cards for the money July 2010, the 5850 gives exceptional performance at 1920 x 1200 in most games. The 5830 gives just great performance.
http://www.tomshardware.com/reviews/gaming-radeon-hd-ge...
I would go with a EVGA GTX460, probably the 1gb version when it is released. The 1gb version will have a lifetime warranty vs. 2 years, and EVGA support is very good. If you ever want more, I would favor graphics upgrading by selling the old card and replacing it with a single stronger
2) CPU. What cpu is required to drive such a card to good frame rates? Tom's did a nice article "is i3-530 fast enough for performance gaming?"
http://www.tomshardware.com/reviews/core-i3-gaming,2588...
The conclusion showed <4% difference in FPS overall in all of their tests using a 5850. The other cpu's included i7-870, X3-720, X4-965 at stock. The 530 is a great overclocker. When overclocked, it matched the stock X4-965.
At $115 it is a good CPU, and the 32nm mfg. technology keeps it cooler. If you have games or other apps that thrive on 4 or more cores, like FSX or Photoshop, then a quad would be better.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
3) Psu.
The GTX460 requires a psu with 450 watts, and two pci-e power connectors. Not much else is important. My short list of quality psu brands would include Corsair, Seasonic, PC P&C, XFX, and Antec. You can pick any one of them. The price point will be about $80. You may find one for a bit less. But, don't be tempted to go with a cheap psu of unknown quality.
My pick would be the XFX 650w unit for $80 after rebate:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
There is a lot to like. Bronze efficiency, modular, and well reviewed.
4) motherboard.
Almost any 1156 based motherboard will do. All will have at least modest overclocking potential, except perhaps Intel. My short list of vendors would include EVGA, Gigabyte, and ASUS. Look, perhaps at a Micro-ATX motherboard, they are less expensive. They will have 4 expansion slots instead of the 7 on a full ATX format. Today, you get all the extras like many usb ports and sound integrated.
How about the EVGA micro-ATX board for $70 after rebate?
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
5) Ram.
4gb seems to be the good amount for normal operations. A 4gb kit (2 x 2gb) of DDR3 ram should cost you <$100. Do not pay extra for faster speeds or lower latencies. Synthetic benchmarks show nice performance, but it does not show up in more FPS or better application performance. Think 1-2%. Check that it is on the motherboard's ram QVL list or the ram vendors configurator showing that it is compatible with the motherboard.
6) Case.
Almost any case will do. Look for one with at least two 120mm input or exhaust fans for adequate cooling.
The Antec 300 illusion model is a great case at a reasonable price of $70.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
For less "bling" the 200 at $50 with free shipping is a great value. Check shipping on cases, they are heavy and shipping can add $20 to the cost.
If you want a small micro-atx case for gaming, look at the Lian li PC-V351 at $99:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
7) Cpu cooler.
The 32nm cpu's run cool, and really don't need a oem cooler. However, I recommend one. It will allow easier and higher overclocks, and will keep the noise down better than the stock cooler. Almost any will do and be better than the stock cooler. You should be able to find a good one for <$40.
8) OS.
Windows-7 home premium 64 bit seems to be the way to go. It will cost you $100. If you are a student, look into academic pricing for about $30.
The rest of the components such as keyboard, mouse, monitor and dvd are relatively standard. Pick what you want there.
This build will total approximately $700.