Excellent choice!
I think a common misconception is a real difference between UNIX and Linux (and BSD, and so on...). The true UNIX, as a pure operating system, no longer exists, as it is , as Neo so eloquently states, an "architectural philosophy, not a product".
In my learning experience, I have found Linux (particularly RedHat) to be the most friendly. There are tons of programs, scripts, and documentation available for just about everything. Other prefer different distributions of Linux, different vendors of UNIX, or even specific versions of those packages. If you go the RedHat route, I can recommend the RedHat Bible. It takes you from installation to administration, and includes a copy of the installation and software/source disks. If you fancy something else, check out
www.cheapbytes.com. No matter which UNIX you select, you're bound to find great books at most major bookstores that will help you out with it.
Good luck, have fun, and post back to let me know how you're doing!