IMHO, try a Ubuntu derivative. You can do straight Ubuntu, or there's a bunch of variations. Personally, I would recommend
Mint as it comes with all the media codecs, flash plugin, etc pre-installed (so you can hit up YouTube, synch your iPod, play a DVD etc straight off the bat), Ubuntu excludes these by default as it is against their philosophy to include proprietary software - although you can still install them easily enough.
Now, how will you run the Linux OS? Do you have a dedicated machine, do you want to dual boot with your current OS, or use a virtual machine to run it
inside your current OS? The latter would be my recommendation, you can keep using your current OS and just alt-tab over to the Linux OS like you would with an application. I use
VirtualBox (VMWare is nice(r) but it costs).
Oh I should mention that a lot of Linux distributions offer a Live CD which means you can boot the OS straight from the CD and use it without installing. It's slow, due to CD-ROM I/O, but it's painless.
As for learning the OS, you just have to jump in! It helps if you have "something to do", for example, setting up a Java development environment, or a file/web server, or .. well anything really. The first thing I always do is configure the desktop environment and install a graphics driver.
There's plenty of resources on the web, a great place to start is
Ubuntu Forums, there's a wealth of information there, and a lively community that's willing to help, and not just with Ubuntu although that's obviously their focus. You'll also want to get familiar with "man(ual) pages", and the command line in general. It's not necessary for a lot of things, but it is very powerful. Type, for example "man grep" in a terminal for the manual page on the grep utility (grep searches files for a given text).
It's a great OS, if you have an interest, I'm sure you'll enjoy the learning!