The wizard Gandalf would be an obvious character for Harry to interact with. They are both wizards, though from different worlds. They could share their knowledge of magic, and Gandalf could guide Harry in the ways of Middle Earth while Harry could introduce some new magical concepts to Gandalf.
Harry might also interact with Aragorn. Aragorn is a great leader, and Harry could offer his help in the battles against the forces of evil. They could become friends, and Aragorn could teach Harry about the ways of the men in Middle Earth while Harry could show Aragorn some of the wonders of magic from his world.
He might interact with Luna Lovegood. She's always open to new and interesting conversations, and she could approach Harry when she sees him alone.
Obviously, Buffy would be a major character he'd interact with. They could start off as wary of each other but then grow to respect one another's fighting skills. Giles too, as he has a wealth of knowledge about the supernatural, and he and Harry could have some interesting discussions about different types of magic.
Maybe Harry could use his magic skills to face the various challenges in Middle Earth, like fighting orcs or helping the hobbits on their journey.
In this fanfiction, Harry might meet students from various backgrounds. There could be students from far - off magical lands who have their own unique cultures and magic. He could also run into some Beubaxtons alumni who come back to visit and they might share some interesting stories or give him some advice on how to make the most of his time at Beubaxtons.
He could meet his future self. This would be a very interesting encounter as he could learn from his future self about what he has accomplished and what mistakes he should avoid. He might also meet the future generations of his family, like his grandchildren or great - grandchildren.
Perhaps Harry will run into an old wizard who has been in the hospital for a long time. This wizard has a lot of stories about the old days of the wizarding world and gives Harry some valuable advice.
Well, he might be really confused at first. Middle Earth has its own unique magic system and races. Harry, with his Hogwarts - trained magic, would have to adapt. He could probably make friends with some of the elves, like Legolas, as they both have a sense of honor and skill in archery. And his encounter with Gandalf would be really interesting, as they are both powerful wizards in their own ways.
Obviously, he would interact with his father, James Potter. They could form a bond that Harry never had the chance to have in his own time. He would also meet Sirius Black, Remus Lupin, and Peter Pettigrew, the other Marauders.
There are many potential characters. The teachers at Forks High School for sure. Harry could have interesting conversations with them. Also, if there are any other supernatural beings in the Forks universe in this fanfiction, like werewolves, he could interact with them. And of course, the students who are into different clubs and activities at the school. He might bond with the science - loving students or those on the school newspaper team, sharing his own experiences from Hogwarts in a veiled way.
Maybe he'll run into a group of young witches and wizards who are on an adventure of their own. They might team up with Harry and together they explore the new country. There could also be a wise old witch who lives in a secluded magical cottage and gives Harry some valuable advice about the country's magic and its history.