Something to keep in mind is that each distro is based on a different version of linux. That core version is really what matters. The rest is superficial (not unimportant, just more about preference). That core version will determine which programs will be available to you (unless you want to compile your own, but I've never had success with that).
For example, Ubuntu and Mint are based on Debian.
From my experience, Debian has the most programs available that I wanted to use and the best compatibility with games.
I use Crunchbang ++, which is a lightweight distribution that uses the openbox window manager (instead of something like KDE or Gnome). It's not as easy to use, but it's faster. Since it's based on Debian, I can also run games on it.
Examples of core distros that a lot of other distros are built on (of fork from):
Debian
Red Hat / Fedora
Arch
Slackware
And then there are other versions that are kind of their own thing, but function very similarly to linux, like:
OpenSuse
OpenBSD
For simplicity and learning linux, I'd recommend either Ubuntu or Linux Mint. I tried both of those initially, but that was a long time ago. At one point Ubuntu changed their default user interface to make it "simpler", but less functional and I ditched it at that point.
I've installed Linux Mint on computers for non-computer savvy people and they were able to use it without problems.
There's a comparison page of Linux distros that gives information like that (what kind of installers it uses, what it's based on, etc). It's on wikipedia:
https://en.wikipedia.org/wiki/Comparison_of_Linux_distributions