Generally speaking, I think you should pick a version that you can install.
Once you install it, you'll have a desktop with nice programs that you can use, and it's easy. So then you might be interested in the organization of the filesystem, and some basic terminal commands. (There's nothing interesting about using Linux software, especially considering that FireFox, jEdit, Emacs, Vi, Opera, and OpenOffice all pretty much have the same interface as their Windows counterparts. The software is generally user friendly, at least until it stops working.)
There's not really much to learn, and it seems simple once you've done it. I guess I don't understand the idea of "learning an operating system," because there's no way you could ever understand the ins and outs of all the parts and applications of the entire operating system. (Not even if you're Linus Torvalds.)
So I guess there are four basic parts to "Learning Linux":
1. Understanding the structure of the file system. (My knowledge goes no further than that I know there exists a "home" directory, which I don't leave unless I'm on vacation.)
2. Understanding how file permissions work.
3. Knowing some command line commands, and being able to figure out how to install software that's distributed as source code.
4. Being familiar with the software on your computer.
Part 1 I don't really care about; I just avoid touching my file system.
Part 2 is necessary to understand.
Part 3 is sort of necessary, and as far as installing software goes, that doesn't usually require more than looking at a README file and following directions.
Part 4 is of course necessary; random button pushing never solved anything.