Well, for Toxapex in the story, I'd say a great moveset is Venoshock, in addition to Recover, Toxic Spikes, and Haze. Venoshock deals more damage when the target is poisoned, which pairs well with Toxic Spikes. Recover, of course, is there to keep Toxapex alive. Haze can be used to clear out any stat changes on the field, which can be really handy in certain story battles.
One effective moveset for Cofagrigus could be Shadow Ball, Will-O-Wisp, Protect, and Toxic. These moves give it a mix of offensive and defensive capabilities.
Toge Inumaki is important too. His special cursed speech ability makes him stand out. Also, the principal of the school, Masamichi Yaga, is likely to be important as he is in a position of authority and has an influence on Gojo and the other students. There could be other characters like the members of different clans that also play roles in the complex web of the story.