On my PC parts checklist I try not to tell you which brand of pc parts components you should be buying, allowing you to research your decision on your own. Historically, for folding projects (specifically Folding@Home), support for Nvidia graphics chipsets has been more consistent than for its main competitor, ATI.
Folding@Home is a distributed computing project, which basically means its a project that uses a voluntary network of computers to work on a big project. Instead of spending money on building a super computer, people can download software that in effect allows them to donate idle computer time to accomplish something big. Folding@Home uses your idle time to work on medical research for proteins to treat and cure diseases, coordinated by Stanford University.
You can download free folding software from Stanford. You will need a network connection to download a work unit to start, and upload a work unit that's finished. (While you don't technically need a 24/7 Internet connection, having one will allow your computer to always have a work unit instead of doing nothing.) You can use the default install or customize your setup. Guides are on the official web site.
Folding@Home award you points for finishing work units. Finishing work units quickly lets you earn a lot more quickly, and many people apply their points to a folding team. Using your computer 24/7 at full speed could increase your monthly electric bill, and $50+ or more a month is not uncommon. You're donating computer time plus footing the elecric bill yourself, so most people getting into folding try to pick graphics cards (usually Nvidia chipsets) to get the most points possible per dollar they spend on their electric bill.