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Assuming a realistic Pokemon setting I wouldn't limit myself to just one type especially since a lot of my favorites aren't limited to just one type, but if I had to pick one to make a gym around I'd do an Ice type gym.
Initial party - Sneasel, Cloyster, Froslass
Rematch party - Abomasnow, Cloyster, Mamoswine, Glaceon, Weavile, Froslass
Main - Froslass
TM - Frost Breath, or if we're not being limited to real TMs, Freeze Dry
Gym aesthetics would be a standard ice-type slippery floor puzzle, but with switches located in parts of the gym that when pressed will turn on high-powered fans which push you in a certain direction when you cross its trajectory.