Normally I'd say tuck the shirts in because I think it looks better most of the time. BUT (didn't see that coming did you) it depends on the shirt, the kilt and the situation.

With sport kilts you can get away with a more casual look than with a wool kilt, I think especially since you can do away with a belt.

Also since you will be performing in the kilt, you will need unrestricted movement so I'd say go with untucked or a shirt with an extra long tail that can stay tucked in but have lots of leeway for movement. But untucked will make it easier for you to do the "Hulk Hogan" shirt rip when you win!!

Oh yeah, and where are the action shots of you wrestling in the kilt?