Definitely Hagrid. Hagrid has always been around Hogwarts and has a connection to the students. Sirius could interact with Hagrid if he goes back in time. Maybe Hagrid could help Sirius in some way, like providing shelter or information. And Bellatrix Lestrange could also be in the picture. Since she is part of the Black family, Sirius might have to deal with her in the past, either to try to change her or to stop her from doing something evil.
Obviously, Harry Potter and Sirius Black are the main characters. Harry is the time - traveler, and Sirius becomes his mate in this new timeline. Other characters like Dumbledore are likely to also play important roles, as he is always involved in matters related to Harry and the greater good of the wizarding world.
Naruto would be a very likely character to interact with Hinata. Since they have a strong connection in the original story, in a time - travel scenario, their relationship could develop in new and interesting ways. Maybe Hinata could be more open with her feelings earlier in time.
His father's friends, the Marauders, are very likely to interact with Harry if he goes back in time. He could become a part of their group, learn their secrets, and even participate in some of their pranks. Hagrid is another character. Harry has always had a special bond with Hagrid, and going back in time, he could strengthen that bond even more. And of course, Snape. Harry could try to change their relationship from the start and understand Snape better.
Bellatrix Lestrange could also be a character who interacts with Snape. If Snape goes back far enough, he might try to influence Bellatrix's path and keep her from becoming such a devoted Death Eater. This could have a major impact on Voldemort's power and the overall balance of the wizarding world.
One great fanfiction with this plot is 'Time's Redemption'. In it, Harry uses a powerful time - turning spell he discovers in an ancient book. He has to face many challenges in the past, like avoiding detection from the Ministry's time - turner regulations. Another good one is 'Back to Save Sirius'. Here, Harry teams up with Hermione and they use a secret time - travel device left by Dumbledore.
One of the most common characters is definitely her father, Ned Stark. Since Sansa has the chance to go back in time, she would likely interact with him a great deal to try and change the course of events. Another is Arya. They could team up and use their combined knowledge and skills to make a difference. And of course, Littlefinger. Sansa would be more aware of his manipulations this time around and might interact with him in a more strategic way to outwit him.
Well, sometimes in these fanfictions, a plot twist might be that Sirius goes back in time and discovers a hidden truth about his family. Maybe he finds out that there was a secret alliance or a hidden enemy within the Black family that was influencing events all along. This could completely change his perception of his family's past and his place in it. Also, he could go back in time and end up being involved in a different kind of magic that was lost in his original time, like an ancient form of magic that has the power to either save or destroy the wizarding world.
There could be unforeseen magical consequences. Time - traveling is a tricky business in the wizarding world. By changing Sirius' fate, Harry might accidentally create new problems. For example, the balance of magic in certain areas could be disrupted. There might also be changes to the Hogwarts' community. Students and teachers who were affected by Sirius' situation in the original timeline might act differently.
Harry Potter could be a supporting character. He might be initially suspicious of Draco living with Sirius but then come to understand the situation. Hermione could also be there, trying to help Draco with his studies and also guiding him morally. Ron would probably be the one with the most doubts, but his loyalty to Harry and Sirius might make him tolerate Draco's presence. Lupin could be another supporting character, as he is a friend of Sirius and could offer his wisdom in dealing with Draco.
Definitely Hermione. Since she's Harry's closest friend and very intelligent, she would be deeply involved in any changes Harry tries to make. Also, Snape. Harry's actions in the past could completely change his relationship with Snape. And of course, Voldemort. If Harry goes back far enough, he could potentially stop Voldemort's transformation into the evil wizard he became.