Redemption is a very common theme. Since Loki has a rather villainous past in the original lore, many fanfictions focus on him trying to make up for his wrongdoings and be accepted as a good guy by the Avengers.
Thor would be a likely candidate. Since he is Loki's brother, he already has a connection with him. Thor might be the one to convince the other Avengers to give Loki a chance and be the first to reach out and try to befriend him in this new situation.
One great story could be where Teen Loki has to team up with the Avengers against a common enemy. Maybe an ancient Asgardian threat resurfaces and Loki, despite his mischievous nature, realizes he needs to work with them. In this fanfiction, Loki uses his magic in creative ways to help the Avengers in battles they couldn't win on their own.
There's a fanfiction titled 'Good Loki Among the Avengers'. It's about Loki being sent to Earth as a sort of undercover agent for Asgard but ends up really bonding with the Avengers. He uses his trickster skills for good, like helping them outwit villains in really clever ways. It's a great read if you like to see Loki in a more positive light within the Avengers' universe.
One interesting fanfiction could be 'The Avengers' Unlikely Rescue'. In this story, Loki gets into a situation where he's in over his head, and the Avengers, despite their past differences, come to his aid. It delves into the complex relationships between the characters. For example, Thor is torn between his loyalty to his brother and his newfound comrades in the Avengers. The story might also explore Loki's reaction to being saved by those he once considered enemies, adding an interesting layer of character development.
Future Loki might interact with the Avengers in a cautious way. He knows their past opinions of him and tries to prove himself. He could start by sharing small bits of useful information. For example, he might tell Iron Man about a weakness in a new enemy's technology.
Loki's character development can also involve him learning about the value of teamwork and friendship. As he interacts with the Avengers more, he starts to see the benefits of working together rather than against them. He might share his knowledge of magic and Asgardian lore with the team, which in turn helps them in their battles. This exchange also helps him grow as a character and become more integrated into the group.
In this fanfiction, Loki might interact most with Hulk. It would be an interesting dynamic as Loki is a master of manipulation and Hulk is, well, the Hulk. Loki could either try to use Hulk for his own purposes, which would be very dangerous, or he could end up on the wrong side of Hulk's anger. But at the same time, it could also lead to some unexpected moments of understanding or at least a begrudging respect between them.
He would probably interact a lot with Thor. Since they are brothers, there is a pre - existing relationship full of complexity. Also, he might interact with Iron Man quite often. Tony Stark's sarcastic nature and Loki's trickery could lead to some really interesting exchanges, either in the form of verbal sparring or working together on some high - tech and magic - combined projects.