I'd do either a Fire or Dark team. Fire:
Blaziken (Fire | Fighting)
Talonflame (Fire | Flying)
Chandelure (Fire | Ghost)
Volcarona (Fire | Bug)
Magmotar (Fire)
Rotom (Fire | Electric)
My puzzle would be based on pushing rocks into volcanoes to stop them from erupting. Once a third rock is pushed into the final volcano, a doorway opens up into a cool room where I will be standing in there. With a click of my fingers, the arena lights up and surrounded by a wall of flames.
Dark:
Greninja (Water | Dark)
Malamar (Psychic | Dark)
Scrafty (Fighting | Dark)
Drapion (Poison | Dark)
Bisharp (Steel | Dark)
Honchcrow (Flying | Dark)
My dark puzzle would be based off having to find a key. Each room has various Pokemon which are to be approached and a battle ensues with that Pokemon. One Pokemon will have a key which leads down into the basement of the Gym, where I will be in supreme darkness.