I'm kind of in the same boat as you as far as just starting out in linux. I have no idea whether the AMD has any effect on distro compatibility (I'm on a p4), but here is my .02:
If you're considering Linux support/admin as a career path, make sure you focus on RedHat and/or Suse. Tinker with other builds all you want, but most of the corporate money is concentrated on those 2 distros.
I installed RedHat 9 and Slackware 10 so far, and hope to add Debian when I get a bit more experience. RedHat's install/config has been intentionally designed to be user-friendly to the point that you don't learn much setting it up (Suse seems the same, though I've used it less). Slackeware doesn't hold your hand quite as much, but at the same time it's not too hard and there's good documentation
(Here's a good Slackware install tut, btw)
Whichever distro you choose, install Firefox once you get up and running. Aside from being a cool browser, it's a good way to learn basic installation and file-system skills - and it's well documented. Also try downloading a new theme (KDE-look.org if you use KDE). It also will force you to learn some basic skills. Change your monitor resolution (RedHat always comes up in 800x600 for me, and it's not so simple to change).
Everyone learns in their own way, but I found books don't do much for me - they're good references but practice, mistakes, and repetition is the only way I learn. By focusing on things I like --customizing my desktop, in this case-- I learn a bit without getting bored.
Good luck.