Use what other people you know have. You'll probably run into the same issues that they did, and they'll be able to help you.
If you're interested in seriously learning Linux for Unix' sake, I'd suggest Slackware or a *BSD. BSDs aren't Linux, but fundamentally, either way you're going to get something that's closer to a traditional "unix" experience with very few preconfigured services and no fancy admin consoles to do all the work for you.
OTOH, all the commercial Unix systems have fancy consoles to do all the work for you.
Software Package management is a big weakness with all the Linux distros. Gentoo does it right, with a BSD-like system, and Debian has apt-get, which itself sucks less than Redhat's rpm. Or you could ignore the whole thing and do macho-man compiles from source. Hands down, package management is the biggest frustration for techies running Linux (on the desktop side, I'd say the inconsistencies in UI are probably the worst thing).
If you want something where everything is already done for you and everything works in a desktoppy fashion, that'd be SuSE, or Knoppix if you aren't even willing to make the commitment of formatting a hard disk. SuSE isn't quite a commercial player in the US, but since it's now owned by Novell, that'll be changing.
For commercial interests, and for current widespread industry support, RedHat is the guy to know. Small Businesses generally know RedHat if they know anything about Linux, and RedHat offers good support for its OS, if you've got the cash. RedHat is distinctly NOT desktoppy. It doesn't even ship with an MP3 player among all the packages you can install. It's presently the "business linux", and it's what I run on my machines at home.
Another option in the desktop department is Mandrake, which is free (SuSE costs money), fairly common among hobbyists and IMO a little bit flakey in comparison with everybody else (e.g. problem with LG CD drives, occasional extra RPM hell for being similar to, but not exactly like RedHat).
Debian is a decent intermediate choice. I'm not a big fan of its community, but it is flexible enough as a "server" or "desktop" linux, and it has apt-get which, once again, is a big step up from RPM.
Beyond that, there's dozens of specialized Linux distros. Some are made for newbs (Lindos, Lycoris). Some are specialized for multimedia (EvilEntity, MoviX). Some are set up to be Diagnostic tools (SystemRescue) or for networking functions (Smoothwall). It just depends on what you want and what you want to do.