Gentoo is not difficult to install, you just need to be able to read in one of the languages that the docs are provided in, a feat that many people manage not to be able to do.
Any linux will do for running a game server, I'd recommend not
Fedora as it's a tad bloated and won't give you the low latency that you'd want from a game server. I'd say go for something lean but source-based may be a little too much for a newbie. First of all, check that the games you want to host have server versions available for linux and then if it does, just pick a random distrobution and install it