I would guess if you use a standard install you can select packages and deselect everything you don't want. If you're comfortable with Fedora already, you may try CentOS which is a free clone of Red Hat Enterprise Linux. The install options probably are more straightforward for no gui installs since Fedora is aimed more at the desktop.
Personally, I'm more comfortable with Debian. I can download a 140MB
netinstall CD and deselect everything. Just install a standard system. Then I do
aptitude update and
aptitude install packagename (like apache2, etc). If you go this route, I would install
Lenny since it's going to change to stable soon. Just make sure your /etc/apt/sources.list points to lenny, not "testing"... Here's a good link to a Debian
howto from the command line.