Fedora or Ubuntu
Mimermonk made a good suggestion.. Ubuntu is ideal for beginners.. but I urge you not to stay hooked to it for long. Move on, after learning the basics.
If you'd like, you can dive right into Fedora Core 6 (zod).. which is also user friendly to my opinion, and experience with it. It is also so (very) customizable.
Do you only have 1 hard drive? If you have several, then just install it on a whole disk to save yourself some time.
I've used both Fedora and Ubuntu…in my opinion, someone who is looking to get very indepth with Linux in the future should not start out with Ubuntu. Yes, it is a very easy linux distro to use and the package management systems built into is are very impressive…it is very stable (thanks to the Debian core structure). But I have a few qualms with Ubuntu…the main one being that it does not come with the compiler/build system (build-essentials) by default. The other main problem I've had with it is that it is a very bloated distro.
Don't get me wrong, I love Ubuntu…the bloated issues are inherint in Fedora as well. But if you are planning to use Linux in the long-run, you need the compile/build system to learn the tarball system.
But what do I know, I use Slackware as my primary distro :P.