Be genuine. Just like the fan who was sincere about their love for the artist's work. Don't try to be someone you're not. Share your true thoughts and feelings. Also, show your value. If you can offer something interesting or useful, like the student with her intelligent questions, it increases your chances of success.
Minato might also be a prominent character. As their teacher, he can influence the way Obito and Kakashi interact. In some fan fictions, he could be the one to help them resolve their differences or provide some crucial information about their past that changes their current situation.
Some fanfictions might explore the emotional aspect of their fight. For example, how their past friendship affects the battle. Maybe Kakashi hesitates to strike a fatal blow because of their shared history.
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.