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.
I'm pretty sure they don't fight. The comic's plot doesn't include a battle between them. Maybe in some alternate version or fan-made story, but not in the official comic.