Another option could be Jacob. As a werewolf, he has a connection to the spiritual side of the Twilight world. He might be the one to discover the hauntings first and have to figure out how to deal with them, especially if they pose a threat to his pack or the people he cares about in Forks.
It could be a new character entirely. Maybe a young vampire who was turned recently and is still adjusting to the 'alive inside' state of being undead. This character could struggle with the morality of being a vampire while also trying to fit into the Twilight world's complex social structure.
Aro could be an interesting inside man. He's a powerful vampire in the Twilight series. If he were to pretend to be on the side of the Cullens while having his own hidden motives, it could create a lot of drama. He could be secretly plotting to take over their territory or gain access to some special power that the Cullens possess.
Most likely, the main characters would include the haunted angel itself. And of course, characters from Twilight like Bella, Edward, and Jacob are likely to be part of it as well. They would interact with the angel in different ways, depending on the nature of the fanfiction.
It could be someone completely new. A character that the author creates to disrupt the status quo in the Twilight universe. This new character might have unique powers or abilities that change the course of the story.
It could be a new character, like a young girl who has just moved to Forks and discovers she has psychic powers. She then gets caught up in the existing drama of the twilight world.
One idea could be that the main character starts seeing the ghosts of the vampires' past victims within the Twilight world. These ghosts could be trying to warn the character about some hidden danger related to the vampire clans. Another could be a haunted location in Forks, like an old mansion, that has a connection to the werewolves' history, and the characters have to uncover the mystery.
Perhaps it could be a minor character from Twilight who somehow ends up in a situation where they are kidnapped by a creeper. This would give the writer a chance to explore that character more deeply and in a completely different context. For example, a character like Jessica from Twilight could be the main character. She's not a central figure in the original story, but in this fanfiction, she could have a whole new adventure.
An old werewolf who has decided to retire from the pack life and goes on a trip to all the places that were important to the werewolves in the Twilight story. Along the way, they might run into some vampires and have to face old prejudices and form new alliances.
Edward Cullen could be a great main character. Since he is already a part of the Cullen family who loves baseball, he could be the one to hit a crucial home run. Maybe this home run is what saves Bella from some sort of danger during a baseball - related event. For example, the Volturi might be there to cause trouble during a game, and Edward's home run distracts them long enough for Bella to get to safety.
A new character could be introduced as the main character. This character could move to Forks and be unaware of the supernatural world there. Their arrival could trigger a series of events that force the existing Twilight characters to have a fresh start in how they deal with their secrets and relationships.