It's not like your RedHat computer will explode the day RedHat ends support. I personally think that RedHat is a decent distro for a newbie. Also, if you learn one distribution and how it works, you could easily get along with the others.
My recommendations to you are:
o Make sure to keep your RedHat installation as current as possible using up2date until RedHat pulls the plug.
o Start poking around. Begin with the easy-to-use tools for system settings under X.
o Start looking at the configuration files. Most (all?) of the fancy tools actually edit the configuration files for the system. You will find lots of those files under /etc/
o Learn to use one of the text-mode editors in Linux, either emacs or vi. I have always used emacs, so I would recommend that one. I'm sure other people around here have a different opinion.
o Important point:
If you plan to mess around a lot, do that on a computer that's not vital for you. I have an old Pentium 166 that I got for free. I can screw up that machine royally if I want to. Then I just reinstall it.
o When you don't understand a thing about what's happening
and you've given up. Come back here and ask a question.