If you are new to *nix, I would recommend Ubuntu as it is very user friendly and will be a good gradual introduction to the *nix environment.
If you are bit more skilled and have some experience with *nix, then I would say go for either Debian or Arch. Arch is lightweight and can be customized to your precise needs, but it can be kind of a hassle to install and will definitely take some time configuring things. Also, arch has a pretty awesome forums/wiki that can help you a ton when you get issues. On the other hand, Debian is as stable as an Asian husband and the packages are well integrated, making it more robust.
Of course, BSD is another route to consider, but I've got almost no experience so the only two cents I can give on that is to consider all of the possible choices, even if it isn't Linux.
Good luck finding your flavor!