I just followed some instructions I found for steam tinker launch. I do remember having some issues getting it working at first, but I got it up and running and it's been working since. Can't remember exact steps though, I'm afraid.
If you're going to be using the script extender, some of the most obvious mods to check if it works are Native Camera Tweaks and WASD. They're also, IMO, some of the most important mods to improve the experience.
Might try asking the several Linux communities, they might have some tips based on your specific setup, if you're cool sharing log dumps and config files.