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.
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.
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 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.
Bella Swan is extremely important. She is the central character around whom the story revolves. Her relationship with Edward and Jacob is what drives most of the plot.
Edward and Bella are still very popular in Twilight fanfic. Their complex relationship gives writers a lot of material to work with, whether it's exploring different versions of their love story or what would happen if things had gone differently in the original story.
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.
Robert Sullivan is also a great choice. His leadership skills and his own personal demons, like dealing with past traumas, can be explored in fanfic. His relationships with the other members of Station 19, both professional and personal, can add depth to a story.
Pongo and Perdita are often popular. They are the parents of the 101 dalmatians and have a strong and loving relationship. Their leadership within the family and how they protect their puppies can be explored in many different ways in fanfic.
Dallas Winston is a favorite among many. His tough - guy exterior but complex emotions underneath are really interesting to write about. Fanfics can delve into his past that made him the way he is and how he really feels about his friends in the Greaser gang.