A question about quest maker

When you choose your enemies do you choose their movesets as well?

Cause if so I need to talk with Shiny

You have the option to either use a preset character or a custom character for both sides. For custom, you basically are using your version of the character; moveset, equipment, etc.

Also of note; Chaos (the normal one) is able to be used as an opponent in quests, and you choose one form instead of fighting all three.