Hiruzen Sarutobi is definitely one of the most important. As the Third Hokage, he has a wealth of knowledge and power. His actions and decisions have a huge impact on the clan and the village. Another important character could be Asuma Sarutobi. He is a skilled ninja and his relationships with other characters, like Shikamaru, add depth to the fanfiction.
One idea could be exploring the early days of the Sarutobi clan. Maybe show how they developed their unique jutsu. Another could be a story centered around a young Sarutobi clan member who has a rare ability and must prove themselves in the Hidden Leaf Village.
One possible plotline could be Naruto growing up with a different set of values and training methods. Instead of the rough start he had in the original story, he'd be mentored by the Sarutobi clan's elders. He might learn more about the history and secrets of Konoha at an earlier age, which could lead to him being more politically aware and better equipped to handle future threats. For example, he could be trained in unique Sarutobi jutsu from a young age, giving him an edge in combat.
His character would likely be more refined. With the Sarutobi clan's influence, he'd have better access to knowledge and proper guidance. He might not be as brash as in the original story. For example, he'd learn the importance of diplomacy and strategy earlier.
In this fanfiction scenario, Naruto might learn unique chakra control techniques from Sarutobi. Sarutobi, being an experienced ninja, could teach Naruto how to better manage his large chakra reserves. This would lead to Naruto being able to perform jutsus more efficiently and with less waste of chakra.
I really like 'Sarutobi's Unseen Trials'. In this fanfiction, it focuses on the political aspects that Sarutobi had to deal with in the Hidden Leaf Village. It gives a new perspective on his leadership and the difficult decisions he had to make.
Perhaps in this fanfiction, Sarutobi is trapped in a genjutsu created by a rogue ninja. Naruto, being highly resistant to genjutsu due to his Uzumaki blood, manages to break into the genjutsu world. There, he has to fight his own inner demons as well as the rogue ninja's illusions to free Sarutobi.
Obviously Naruto would be one of the main characters interacting with him. Naruto would look up to Sarutobi as a mentor and a source of knowledge. Their interactions could range from training sessions to deep conversations about the future of the village.
It could be that Naruto has a different view of leadership than Sarutobi. Naruto might see Sarutobi's leadership as being too passive or too focused on maintaining the status quo. He, with his more energetic and revolutionary ideas, may resent Sarutobi for not being more progressive in making the village a better place for everyone, including himself.