One option is to have a Decidueye (if you started with Rowlet). It's a strong Grass / Ghost type. Along with a Raichu for Electric - type power. And a Sandslash for its Ground - type moves. This combination can cover a lot of different type match - ups you'll come across in the story.
A fanfiction might focus on Lillie's relationship with other characters in Pokemon Sun. For example, how she interacts with the protagonist and how their friendship evolves over time. They could go on adventures together, and Lillie could learn important life lessons from these experiences. Also, her family background could be explored more deeply in the fanfiction, which could add more layers to her character.
I recommend Torracat (evolved from Litten), Brionne (from Popplio), Dartrix (from Rowlet). Torracat is strong and has good fire - type moves. Brionne is cute and can hold its own in battles. Dartrix has some nice grass - type attacks. Also, having an Alolan Sandslash for its ice - type moves and a Lycanroc for its speed can be great additions to the team.
You can't go wrong with a team of Pikachu, Eevee, Charmander, Squirtle, Bulbasaur, and Pidgey. Pikachu is iconic and has electric - type moves. Eevee can evolve into different useful forms. Charmander is a classic fire - type starter. Squirtle for water - type attacks. Bulbasaur for grass - type moves and Pidgey for early - game flying support.
One possible fanfiction could be about Sun and Lillie going on an adventure together in the Alola region. They might discover a new and rare Pokemon that only appears during a certain lunar phase. Sun could use his skills as a trainer to protect Lillie from any potential danger, and in the process, their relationship could grow deeper.
I think a team of Torracat, Brionne, Dartrix, Alolan Vulpix, Mareanie, and Yungoos could work well. Torracat has good offensive capabilities. Brionne is a cute yet powerful water type. Dartrix is useful for its grass - type moves. Alolan Vulpix with its ice typing can handle certain threats. Mareanie can be a tough defender, and Yungoos is good for its normal - type attacks.
Well, for the story in Pokemon Sun, I'd recommend starting with the starter Pokemon that suits your playstyle, be it Rowlet for its grass - flying type which is useful against many early opponents. Then add a water type like Mudkip (if obtainable) for its versatility. Also, having a normal type like Eevee can be great as it can evolve into different useful forms later. And don't forget about a flying type like Pidgey which can help with scouting and quick getaways. Another good addition could be a psychic type like Abra for its strong special attacks later on.
One possible fanfiction could be about Mallow's journey to discover new and rare ingredients for her cooking. Maybe she ventures into a mysterious forest in Alola and meets a Pokemon that has the ability to guide her to a hidden grove filled with unique berries and herbs that she can use to create a special dish for a big island festival.
Well, in my opinion, a top team for Pokemon Sun story would be Greninja, because of its high speed and strong water - type moves. Then there's Alolan Raichu which is a unique Electric - type. Salamence for its flying and dragon - type power. Garchomp too is a great addition with its high attack. And Gardevoir for its psychic - type abilities. These Pokemon together can cover a wide range of types and battle scenarios.
One possible fanfiction could be about Wicke's backstory. Maybe she has a hidden past as a trainer herself before devoting her life to research in Alola. In the fanfiction, she could discover an ancient Pokemon that has a connection to the history of the Alola region and she has to protect it from Team Skull.