Obviously, Ash is one of the main characters. He is the protagonist who is on the mission to catch Mew.
Obviously, Ash is one of the main characters. He is the Pokémon trainer on a quest to catch Mewtwo.
Pikachu would most likely be there. Since Pikachu is Ash's closest companion, it would be involved in any story related to Ash. Maybe Pikachu could also have some sort of interaction with Mew, like being a bit jealous at first of Ash's new connection with Mew.
In some versions of the 'ash catches mew fanfic', Ash might have a special encounter with a legendary Pokémon trainer who gives him a rare item or some advice on how to catch Mew. This encounter could be the turning point in his quest. And sometimes, Mew itself may be in a situation where it's more vulnerable, which gives Ash the opportunity to attempt the catch.
There are 'Ash Catches Mew' fanfictions where Ash catches Mew accidentally. He might be trying to save Mew from some other danger, like a group of poachers. In the heat of the moment, Mew decides to trust Ash and goes into his Pokéball. This unexpected turn of events then leads to a whole new adventure as Ash has to deal with the implications of having caught such a rare and powerful Pokémon.
Obviously, Ash is one of the main characters as the title implies he is the one trying to catch Kyurem. Kyurem itself is also a main character in a sense, as it is the target of Ash's pursuit. There might also be Ash's Pokémon, like Pikachu, which could play important roles in the story.
Obviously, Ash is one of the main characters as the title implies he is the one trying to catch Meloetta. And Meloetta itself is also a main character as it is the target of Ash's pursuit.
Team Rocket could be the main antagonists. They might hear about Ash's encounter with Mew and try to capture Mew for their own evil plans. They could set up all sorts of traps and schemes to try and separate Ash from Mew and steal Mew away.
Team Rocket could be the main antagonists. They might see Ash's transformation into Mew as a way to capture a powerful Pokémon - like being. They could devise all sorts of plans to catch him, thinking that they can use Mew - Ash's powers for their own evil purposes.
I'd recommend a fanfiction where Ash catches Mew during a battle tournament. In this story, Mew enters the tournament secretly, and Ash is the only one who realizes it's Mew. He manages to catch it during the final showdown. The story is full of intense battles and great character development for Ash.
Obviously, Ash is one of the main characters. He is the trainer who catches the shiny Pokemon. His Pikachu also plays a significant role, as it's always by Ash's side and could potentially have some interesting interactions with the shiny Pokemon.