Test a few the big ones (Fedora and Ubuntu spring to mind), play nice with native package managers and use a liberal enough license that someone can make a pack

Test a few the big ones (Fedora and Ubuntu spring to mind), play nice with native package managers and use a liberal enough license that someone can make a package of your game for another distro, even if they still need to install the data separately. This makes it the responsibility of package maintainers to modify the package you've already made to point at the right directories. Another approach may be to use autopackage or similar.