If you're new to GNU/Linux, I highly recommend
Ubuntu (a Debian derivative) as your starting point. The information below may not be as useful in today's world of "It Just Works" distributions, but it may give some insight into why I'm such an Ubuntu fan...
I'll admit: it took me several tries with several different distributions of Linux to really get the hang of the "new" environment.
In retrospect, two main things were the biggest barriers to my success in those first days and weeks. One was my ignorance of how Linux manages and learns about your system's hardware, and the second (more difficult) obstacle was the dreaded dependency problem inherent in getting new software up and running.
Now granted this was a few years back, and things have come quite a way since, but I still think one of the single biggest factors that will keep a new user interested and coming back to a Linux box is the way its packaging works.
Personally, my first experiences (with Mandriva Linux) and the RedHat Linux RPM packaging system were very discouraging. I had a very difficult time trying to find the information I needed on the web to even get my hands dirty with a basic installation of a new program. Coming from a heavily Windows-influenced background, I needed something that, conceptually, didn't look so much like a missing DLL.
In the end, I went to Debian and then finally Ubuntu (backwards, I know...). The fluidity of the deb packaging system was so much more accessible and
understandable to me. Bottom line: I was finally up and doing things that I knew were possible before that point, but which I couldn't seem to find.
After awhile I become very comfortable with Ubuntu and other UNIXes. One of the reasons I keep coming back to Debian and Ubuntu, though, is their excellent user-driven forums, wikis, and knowledge-bases. It doesn't matter what flavor of Linux I'm using, the simplest and most straight-forward answers always seem to be linked back to
ubuntuforums.org. You should definitely check them out first if ever you need a question answered.
Another suggestion if you're only just starting with Linux: keep it simple. I know that sounds terribly obvious, but if you're like me and you try to jump right into compiling
MythTV from scratch (one of my very first projects...), you're likely to be disappointed with your progress.
So again, download
Ubuntu (the desktop edition), and give it a go.