If you feel troubled compiling programs from source, it's common. There are numerous things that can go wrong, and most often I have found myself figuring out what configure options I need to give before the make step, so it succeeds and lets me do make install afterwards. Since you're using Fedora Core that has binary packets I strongly suggest you install the binary rpm version of MySQL (and Apache):
yum install mysql apache
If your current yum reposities don't include those packages, add such reposities (google and visit redhat.com/fedora for more information). But trust me, you will want to learn a lot from compiling programs, about compilers, versions etc. before you'll start compiling "big things" like web server components. In my opinion you should start off by compiling some smaller apps and get familiar with the process and how you can affect it.