It could be the First Hokage, Hashirama. Naruto would be amazed by his powerful Wood - Style jutsu and his ability to create the village. He could learn about the original ideals behind the Hidden Leaf from Hashirama.
Well, it depends on the specific fanfiction. Some fanfictions might explore alternate storylines where Naruto doesn't become the Hokage at all. Maybe he decides to pursue a different path in life, like focusing on being a teacher or an explorer. However, in a large number of fanfictions, he does achieve his goal of becoming the Hokage because it's such an iconic and desired outcome for fans who want to see his journey to the top in different ways.
Shikamaru is another possibility. He is known for his strategic mind. As Hokage, he could use his intelligence to make wise decisions for the village. He may not have the brute strength of Naruto or Sasuke, but his ability to plan and analyze situations would be invaluable in leading Konoha.
One common theme is redemption. Since Kakashi can go back in time, he often tries to make up for past mistakes or prevent tragedies that occurred in the original timeline. For example, he might try to save a character who died before. Another theme is the changing of fates. He can change the destiny of not only himself but also of his friends and the whole village. He can use his knowledge of future events to better prepare for threats.
His friends like Sakura and Shikamaru would surely support him. Sakura, with her medical skills, could be an important part of his regime, providing healthcare for the ninjas. Shikamaru, being intelligent, could offer strategic advice. Also, the younger generation of ninjas who have been inspired by Naruto would be his strong supporters, as they believe in his leadership and the new direction he could take the village in.
Perhaps a perk is the ability to shape the future of the ninja world. As Hokage, one can inspire the younger generation of ninjas. They can create new ninja academies or training programs. They also have the power to pardon or punish ninjas according to their deeds, which helps in maintaining law and order in the village.
Sasuke could also be a possibility for the 6th Hokage in the fanfic. He has grown stronger over the years and his unique perspective on the ninja world could bring new ideas to the leadership of the Hidden Leaf. He might start off as a controversial choice but prove himself through his actions in protecting the village and making tough decisions.
Sasuke could be an alternative. He has strong ninja skills and a deep understanding of the ninja world. His experiences have made him grow into a very capable person, and his Sharingan gives him an edge in combat and strategic planning.
One possibility is that there would be a lot of reminiscing. Team Minato was Kakashi's old team. They might talk about old missions, like the one where they faced the Stone ninjas. Kakashi could share how their teachings influenced his leadership as Hokage.