CentOS is great, as it's already set up with enterprise in mind. Debian is another rock-solid as was mentioned above. All that said, you could also try Ubuntu Server if you don't mind not having a GUI (which would help the learning process greatly tbh). It depends what kind of server you want, and what you want it for.
For production type servers, you NEED something solid (CentOS, Debian) but for home use the (Linux) world is your oyster. Most distros include server apps, so it's just a case of playing around with what you feel comfortable with. Fedora runs Apache or lighttpd nicely, but is bleeding edge and uses experimental kernels at times so although it's a great desktop/home distro I personally wouldn't use it in production environments.
If you want it to be a dedicated server, having no GUI isn't an issue. If it's a home desktop and you just want to "play" with servers then any distro with apache2 added on with Webmin would be a nice start. You could even set up a virtual machine and try the different distros that way.
I had three servers running inside VMs on three different distros last year, just to play around. PCLinuxOS has an easy to use server with the legendary Mandriva control panel available to configure it. Again if it's a desktop machine playing at server that's worth a look too
Loads of options, just have fun looking around and experimenting. Virtual machines would make it a lot easier, as you don't have to format the hdd every time you want to try a new distro or setup. I found (to my shock if I'm honest) that Xandros Server was fantastic (fast, smooth, well integrated) and easy to use - but that one as a price tag (US$99 iirc).
Hope I didn't confuse you further lol Basically any distro will play server nicely, but some are better than others. I know you said you're fairly new - what have you tried so far?
