as long as you install java as described by java and java is in your PATH then tomcat will have no problems.

install from source VS prebuilt packages

how much are you wanting to learn?

you will get a better understanding of things if you build from source, but if you just want to get up and running and don't care about the guts then install the packages.

also depending on your version of fedora (3 or less) you might want to try apt as noted in my sig