I personally use Linux Mint, and I think that is very popular. It is based on Ubuntu, so I think it’s correct to say that if you target Ubuntu then Linux Mint would be covered.
It seems hard to target a specific distro! Even if there are families (debian, red hat…) there’s just too many variations. Pico-8 works I guess because it’s just looking for the SDL libs in the system search path.
For a standalone game, I think appimage may be the thing that works universally (all distros + after some years)