Naruto would become more confident. Gojo's power is extremely strong, and having it would make Naruto feel like he could handle almost any situation. He'd also become more strategic as Gojo's power requires a different approach to combat compared to his normal ninja skills.
A possible plot is that with Gojo's power, Naruto is able to see the world in a new way. He can now perceive curses in the ninja world that were previously hidden. This leads to a whole new side - quest where he has to deal with these curses while still maintaining his duties as a ninja. He might also use Gojo's power to teach other ninjas a new way of fighting, changing the ninja combat system.
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.