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.
Bella Swan is also a favorite. Fanfiction might explore what would happen if she was reborn as a vampire right from the start. It could change her relationship with Edward and the other characters in many ways.
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.
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.
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.
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.
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.
Some of the more morally ambiguous characters tend to draw a lot of attention. They are not clearly good or bad. For instance, a character who might steal from one group to help another. Their actions are not always justifiable, but they make for very interesting character studies as readers try to understand their motives in the chaotic world of Twilight 2000.
One of the most popular characters to focus on is likely the main protagonist. His leadership skills and complex personality make for great storytelling. Another could be the tech - savvy character. Their ability to get the team out of tough situations using technology is always exciting to write about.
Andy Herrera is often a popular choice. Her strong leadership skills and complex family background make for great fanfiction material. Writers can explore her relationship with her father, Pruitt, and how she balances her personal and professional life.
Hannibal is often a popular focus. His leadership skills and strategic mind make for great storylines. Writers can explore his past military experiences in more detail or create scenarios where he has to outwit an even smarter adversary.