I'd decide what distro(s) you offer for installation on users machines first, then get as familiar as possible with the specific one(s) you choose, as well as with Linux in general. Perhaps reading books specially targetted at the distro would help. Maybe you could take a course in Linux/the distro(s)- such things exist. In particular, look at what comes with each distribution- particularly the desktop environment or environments it offers. So for example, Vector offers about 5 different DEs/WMs (If I remember rightly from the brief period I had it installed). Obviously, most/all major desktop distros will have extra software, including DE/WMs available in their repositories. I'd generally assume though that if a user knows enough to know the difference between different environments and why they'd want to get another that they understand what they're doing too.
A good set of tutorials for the new can be found at
http://www.tuxfiles.org. Still reading them, and they are proving pretty good help
I also think 2damncommon has a good idea about looking into LFS- even if you don't build your own LFS, I read some of the documentation and it did help my understanding of the internals a little. Perhaps slightly more friendly would be to install Gentoo (from source of course) without the new graphical installer. I found that by following through all the instructions as I went about installing it, I was able to learn a fair amount about Linux "under the hood" so to speak. I also gained a lot of confidence around a few of the common and some of the slightly more advanced command line programs, which can't hurt.
Finally, once your done, break your system in a way a user might concievably manage (and maybe some that they probably wouldn't) and then try to fix it
I have found one of the best things for learning something about Linux in the early stages was fixing the problems when an installation went wrong, or hardware didn't get auto-configured. I fixed my mouse in Ubuntu (with GNOME) by learning the important keyboard shortcuts in GNOME (I didnt' think about dropping to a virtual terminal because I didn't know about them at the time
) to get myself to a virtual terminal.
Good luck
(P.S- After all I've done so far- I'm
still quite a newb. But then at the minute I don't really get much of a chance to use Linux, whereas you will presumably be able to devote a good amount of time to learning