Jiraiya
Of everyone in the Naruto series, the one character who most likely knew Yondaime the best would be Jiraiya. Considering him being the Jounin under the young Yondaime's supervision, Jiraiya most likely understands Yondaime's tendencies the best in terms of being a ninja and being a friend.

Orochimaru
Orochimaru most likely loathes Yondaime for Sandaime chose him to become the Fourth Hokage instead of him. It is beacause of that reason and the fact that there had always been a sense of uncertainty in regards to his sanity that Sandaime most likely choose someone other than Orochimaru. Whether he'd been chosen to be Yondaime or not, it is certain that Orochimaru would continue his researching to develop the new jutsu for immortality.

Tsunade
It is not known how well Tsunade knew Yondaime, however from her speech inregards to the similiarities between Yondaime and Naruto she apparently isn't fond of Yondaime's presence when he was alive.

Sandaime
Sarutobi, Sandaime, was most likely the one who chose Yondaime to become Hokage. Sandaime had originally intended to have Orochimaru to become his sucessor because he knew that Orochimaru had a extroradinary talent which is considered very valuable especially during a time of war. Sandaime knew for a long time that there was something different about Orochimaru's ambitions, however he kept it a secret let it go believing that someday he would change. Even after uncovering Orochimaru's secret test area for his new jutsu, he still had hopes for him, however that mistake he made back then costed him much more. Another thing to note in regards to Sandaime is that he and his summon, Enma, knows of the forbidden technique used to seal the Kyuubi. Perhaps Sandaime was accompanying Yondaime during his last battle.

Kakashi
Yondaime was also a Jounin instructor in Konoha. Luckily for Kakashi and two others, Yondaime was chosen to be his teacher. It is still unknown how well Kakashi knew Yondaime, however it's safe to assume that how Kakashi sees Yondaime is much more different than how the others would.

Naruto
Unbeknownst to Naruto, Yondaime's legacy lies sealed within his body. It was until Mizuki tricked Naruto into stealing the Foribidden Seal Scroll that Naruto was told the truth about his past. Yondaime had wanted the fact that the Kyuubi being sealed in Naruto's body a secret and that Naruto would be known as a hero. The people of Konoha village accepted that request but instead of considering Naruto a hero they shunned him from society.