There's no particular distro preference. If you can install Steam on it, Proton is also likely to work. Steam's SteamOS is Arch based (btw), used to be Debian based. Steam games used to target Ubuntu, I can't find the sources for this, but I remember seeing it as a target. LTS versions usually.

I personally had good experience with either Mint Cinnamon, Debian (with KDE), Fedora and Manjaro, so it's pick your poison, really. For support reasons, I suggest a popular distro.

You can use any distro you like. I'm using OpenSUSE Tumbleweed and have basically the same experience as most people on ProtonDB. The thing to remember is that to use Proton for games that Valve hasn't verified, you have to go into your Steam settings and under Steam Play check "Enable Steam Play for all other titles".

I have noticed that some games work better or worse under different versions of Proton, though.

Just install the steam client and enable compatibility. I always set it to forced experimental to use the most up to date version of proton

As long as it can run Steam. Steam on Linux has Proton built in.