Depends on your access.
Debian IMHO is the most solid of the popular distros but almost all, including RedHat, are very good. Debian is less user-friendly on a desktop machine than RedHat, who have worked quite hard on ease of use. Install is much better on RedHat too, but I guess that's not an issue. They are both very easy to keep patched.
If you just have ssh access to root then you're not going to notice much difference, you'll work both via bash (the command line). If you can access with Gnome/KDE via X11 then RedHat will probably have much better tooling than Debian - as a Unix novice that's a good reason to go for RedHat. However, I guess a "powered by Debian" sticker will give you plenty of Geek-points
