Link is obviously a popular choice. His journey, his skills, and his relationships can be explored in many different ways. Midna is also very popular. Her mysterious nature and her connection to the Twilight Realm make her an interesting character to write about.
Edward Cullen is often a popular choice. His brooding nature and vampire abilities make for interesting storylines. Writers can explore his character further, like how he would react if he was reborn with different memories or emotions.
Jacob Black is also quite popular. His loyalty and his struggle between his love for Bella and his werewolf identity can add a lot of depth to a fanfiction. Another popular character could be Alice Cullen. Her ability to see the future can create interesting plot twists and turns in a story 'into the night' in the 'Twilight' world.
Harry Potter himself could be a central character. His courage and ability to face dark forces could be put to the test in the Twilight universe. Maybe he has to deal with a vampire coven that has some dark intentions similar to Voldemort.
Obviously, Bella, Edward, and Jacob are the main ones. Bella is at the center of the love triangle, so she's always a key focus. Edward with his brooding vampire allure and Jacob with his warm werewolf charm are also very popular to write about.
Renesmee is definitely a popular one. Since she is a new and unique character in the Twilight universe, there are a lot of possibilities to explore with her. Jacob is also popular as his relationship with Renesmee is quite complex. And of course, the Cullen family members like Edward and Bella still hold a lot of interest as they are central to the whole story.
Sasuke is a very popular choice. His complex backstory and brooding personality offer a lot of room for exploration. Fanfictions can delve deeper into his time with Orochimaru, his family's past, and his relationship with Naruto from a different perspective.
The main hero, of course. They are often the center of the action in the original story, so there's a lot of material to work with. You can explore their uncharted emotions or put them in new and challenging situations.
Definitely Catherine Cawood from Happy Valley. Her strong - willed and no - nonsense personality would be really interesting in the Twilight universe. And from Twilight, Edward could be a key character. His brooding nature and vampiric abilities would create an interesting dynamic with Catherine. Also, Bella could be included as she might learn a thing or two from Catherine about being independent.
Jacob Black is definitely a popular choice. He has a complex character arc in the original series and fans often like to explore more of his backstory or his future in fanfics. His relationship with the other wolves and his feelings for Bella can be further delved into.
Edward, even though he is absent for a large part of 'New Moon', still has a big impact on the story. Fanfic might explore his time away, what he was thinking and feeling, and how his return would be different if the story was told from a different angle.