Yes, that card will work fine.
(That board/chipset will only support 4GB max of PC 4200 (533 MHz) and PC2 5300 (667 MHz) DDR2 DIMMs. But as long as your O.S. is 32 bit, 4GB is all you can make use of anyway. 4GB won't be a limiting factor if you use the computer for tasks like gaming.)
For a few dollars more, I would move up to a HD 6790
And if you want to spend your max limit, the HD 6850 is a great mid-range card: http://www.newegg.com/Product/Product.aspx?Item=N82E16814102908
Here's a hierarchy chart to see where the cards fall as to gaming power. Remember, the higher the resolution you game at, the more card you need to maintain good framerates w/ lots of eye candy. http://www.tomshardware.com/reviews/best-graphics-card-gaming-performance,3042-7.html
Any of those 3 cards is great at 1680x1050 and lower. The HD 6850 can even play well at 1920x1080 if you lower the eye candy a bit.