If you are looking for a server, go RedHat or CentOS (a free edition of RedHat). Fedora is too cutting edge and has too short a release cycle.
havea look at the installation manual at www.redhat.com
, but you machine should run it fine without a GUI (which you don't want for a server anyway).
How much space do you need? Depends what you want to do. I'd probably allow more than 4g myself, but it is so simple to do an install (maybe an hour end-to-end) that you could either reinstall or just expand the partion if too small.