Beren, that isn't a bad recommendation. The 5570 has low power requirements for the power supplies that come with dell and gateway machines. It also places on the hierarchy charts with the HD 4670, in fact I believe it is intended to replace the 4670. It would play most games well at 1680X1050 (22inch monitor)
It is a good budget video card.
Without knowing more about you PSU, I think the most powerful card you could handle would bne the HD 5750:http://www.tomshardware.com/reviews/radeon-hd-5770,2446-15.html
MSI has one on sale now at newegg for $99 after rebate:http://www.newegg.com/Product/Product.aspx?Item=N82E16814127460