Goku would be a great choice. He's the main protagonist in Dragon Ball, and the full moon has always had an interesting connection to him. His Saiyan heritage makes him react to the full moon in unique ways. So, a story could be written about him experiencing some new kind of full - moon - related adventure or struggle.
In a 'Full Moon Blues Dragon Ball Fanfic', it could center around the idea of a hidden or lost Dragon Ball that only reveals itself during the full moon. A group of characters, perhaps some new ones along with the old favorites, go on a quest to find this Dragon Ball. Along the way, they face various challenges, like battles with new types of creatures or dealing with the power - hungry villains who also want the Dragon Ball for their own evil purposes.
Goku could be the main character. Imagine Goku being hypnotized and having to fight against the control while still trying to protect his friends and the Earth. It would be a great twist on his usual heroic self.
Gohan could be the main character. Since he has great potential and is intelligent, in this frigid future, he could be the one leading the fight against the cold - related threats. He might use his skills as a scholar and a fighter to find solutions to the problems in this frozen world.
Goku could still be the main character even in a dimension - hopping fanfic. His adaptability and thirst for stronger opponents would make him a great fit to explore different dimensions.
The main character could be a Saiyan gamer who was born on Earth but discovers his Saiyan heritage through the game. He then uses his knowledge of the game to train faster and become stronger than he ever thought possible, kind of like Gohan but with a more gamer - like approach to his training.
Maybe a new Saiyan who was born on a different planet and has a different understanding of Saiyan culture. He or she could come to Earth and interact with the existing Dragon Ball characters, bringing new fighting styles and a fresh perspective to the story.
Goku could be the main character. Since he's the protagonist in the main Dragon Ball series, it would be interesting to see him explore the concept of Souls in the FighterZ universe. He could learn new ways to use his Super Saiyan powers in relation to his Soul.
Goku could be an interesting main character in a vampire fanfiction. Imagine Goku having to deal with the newfound thirst for blood while still trying to protect the Earth. His strong moral compass would be put to the test as he battles against his vampire instincts.
It could be a completely new character created just for the fanfic. Somebody with a booming voice and a flamboyant personality, who loves the thrill of the Dragon Ball Z battles.
It might still be Goku. Since Cell is coming back, Goku would be the one to step up and defend the Earth once again. He would be at the center of the fight against Cell.