I was in a similar situation about 4 years ago! When I had not even started college.

I would firstly forget about the distro switch, this change is something too complicated for a start, especially if you are not used to those particular servers.

You should learn the internals of services running on the machines. Get a spare machine, install the same Red Hat release running on those servers and install the same services. Now try to make them work the same way they are on the servers. This is a shot in the air, but you can start with bind, apache, sendmail (or whatever mta you've got), etc. Google is your friend here, if you look for help about this programs you would find the dns howto, the apache documentation (also installed locally) and a package called sendmail-cf for example.

While playing with this kind of things, you will soon have some problem you can't get along with, you can ask for help in usenet, but try groups.google.com before. 99.99% of times you'll find someone in the same situation, most of the times with a solution in the same thread.

Don't worry for unix/linux basics, while doing this kind of things you'll learn what you need, just be patient. You say you have a "decent amount of Linux experience", so you don't need a basic general linux book, which otherwise would be a must.

After some time with this things, when you have a decent knowledge of the situation, you can improve with books of a particular subject. This depends on the situation, for example, if a samba server is something important for the company, get a book about samba, etc. Manpages or internal documentation are also a good source of knlowledge.

Last but not least, subscribe to a security mailing list, you have to be alert to new security failures, I can't recommend you anyone in english, Bugtraq is too high volume IMHO.

Good luck.