Just pick one and have fun. You can install pretty much any software you want on any distro, "gaming focused" just means some stuff comes preinstalled/preconfigured.

The process to get gaming on pretty much every distro is:

1. Install OS
2. Install Steam and Heroic
3. Download and play games

Your experience will be very similar on whatever distro you choose.

I recommend Mint or Fedora for new users, mostly because they're popular so getting help should be easy. I personally use openSUSE Tumbleweed though, which is also fantastic.

I would personally recommend the base distros and I am a big fan of Fedora myself. Has been rock solid for the last 4 years or so. Although you'll have to choose a desktop environment as well. I use gnome, which imo just looks and feels really good, although it's not as easy to customise. You can also pick KDE, which looks more like windows by default but you have so many settings it's a bit too much imo.
You can always change the desktop later if you really want to, so pick whatever you think you'll like best