A big question this one, especially when trying Linux for the first time. I was lucky that I had a good experience with Mandrake (as was then) but a bad experience could have put me off for life. I know from reading forums that this is a common question. Someone suggested the Linux distribution chooser website so I had a go.

The first choice was OpenSuse, which is my distro of choice after a reasonable amount of experimentation so it seems fairly acurate as far as I am concerned. The questions were also sensible and not offputting for the first timer.  Definately worth a look