Any modern distro should run just fine on it. I personally like Debian, it's what I use and what I install on all the computers I work on for people who don't want to pay for a copy of Windows. Here's some links to some free Linux distros.
Debian - http://www.debian.org
Ubuntu - http://www.ubuntu.com
Slackware - http://www.slackware.com
Mandriva - http://www.mandriva.com
openSUSE - http://www.opensuse.com
Fedora - http://www.fedoraproject.org
openSUSE is based on the corporate product SUSE Linux by Novell, who last I heard is partnered with Microsoft, so there may be a few goodies in there for you, or you may be more limited by somebody that close to our major competition. Fedora is the free version of Redhat Enterprise Linux. It comes without support, but is based on Redhat and runs much of the same software out of the box. Fedora releases a new version every 6 months. Mandriva is another company that sells enterprise versions of its OS, but also releases free versions with or without paid support. Mandriva is also based on Redhat, and was originally called Mandrake Linux, but the name got changed when they merged with Connectiva back in the day. Ubuntu is the major "user friendly" distro that a lot of people use. It's based on Debian, is aimed at general non-techy users, and operates on a 6 month release cycle (Upgrades can be done in place without having to wipe your hard drive and reinstall). The latest version for me was very slow in general and introduced a whole new desktop experience called "Unity", that personally I hated. Debian and Slackware are both very old Linux distros, two of what you might call the "originals". Debian is easier to use than Slackware in my opinion because it has a package management system that allows you to download software in the form of a .deb archive, making software installation much easier than compiling from source code.
Experiment with several, find out which one you like and go with that one. All of these systems are equally powerful, all you're really getting is the people supporting you and the default user experience. All of these can be customized to be just as easy to use and powerful as the next guy, so play around with them and see which one you like, and welcome to Linux!