Get a cheap Dell with a dual-core CPU and 2GB RAM, then throw a Radeon HD 4650 or 4670 in there, because you won't need to upgrade the power supply for that.
If you want to build yourself, you should look at AMD Athlon X2s or the Intel Pentium dual-core series. RAM is cheap, though; you should have no less than 2GB, and might even be able to get 4GB. For a video card, look at the Radeon HD 4670 and GeForce 9600GT. Any cheap, decent Intel or AMD motherboard will do, as will any SATA hard drive.
I also recommend the Antec Sonata III for the case; it comes with a good 500W PSU and newegg has it for $99 with free shipping (shipping is usually like $20 on a case):
http://www.newegg.com/Product/Product.aspx?Item=N82E16811129024