If you have two machines, or one machine and vmware, I'd recommend a bsd. They all have very carefully maintained manuals (outside of the manual pages) that are big enough to teach you a lot but not so big that you can't read the entire things if you're motivated. Pick one, and read the installation section before doing anything else. Then read it again, but do the install on the other machine (or in vmware) at the same time. Then they'll kick you to a command line where you won't have any idea what you're doing and you'll be forced to keep reading the manual to figure anything out. Learn how to install software (ports or packages), how to configure additional network interfaces, how the system starts up and how to manipulate which daemons run, how to build the system from source, how to get a graphical user interface going... (if you're really enthusiastic, read the entire man page for whatever shell you're running) The difference between that and say, Ubuntu, is that in Ubuntu you'll have the snazzy interface right from the beginning that you can fall back on if you don't feel like learning much. That and, in my experience, the community documentation is more geared towards "how do I get this particular thing done?" than "what are the underlying concepts that I need to understand?"
Or heck, do them both. It would be a good idea to get an idea of what is system-specific and what is common to all unixes.