Daenerys Targaryen would be fascinating. She has her own dragons, but Lightbringer could be the key to truly uniting the people of Westeros under her rule. It could symbolize her rightful claim to the Iron Throne and be a tool to overcome any remaining opposition.
One idea could be exploring the origin of Lightbringer in more depth. Maybe it was created by an ancient civilization long before the events of 'Game of Thrones'. Another could be a story where a new character discovers Lightbringer and has to learn how to control its power without succumbing to its dark influence.
Definitely Tyrion Lannister. In a crossover with 'The Simpsons', he could bring his sharp wit and political acumen to Springfield. He'd probably outwit Mr. Burns in no time. His complex personality and ability to adapt would make for a very engaging character in such a crossover fanfiction.
I think Bran Stark could be very interesting too. As the Three - Eyed Raven, he has vast knowledge and powers. In a future fanfic, he could use his powers to foresee and prevent new disasters or to guide the future of Westeros in a more positive direction. However, his new powers might also make him a target for those who fear his influence.
I think Daenerys Targaryen would be really interesting. If she were reincarnated, she could use her past experiences to be an even more powerful and just ruler. She already had a complex journey in the original series, and reincarnation would add more depth to her character. She might be able to avoid some of the mistakes she made in her first life, like trusting the wrong people.
Stormbreaker itself could be considered a character in a sense. If it were to appear in the Game of Thrones world, it would be an object of great power. Many characters would vie for it. It could end up in the hands of someone like Daenerys, who already has a connection to powerful and magical things. This would make her even more of a dominant force in the story.
Arya Stark could be an interesting main character as a summoner. She already has a lot of skills like stealth and combat. If she were a summoner, she could summon the spirits of those she has killed to either help her in battles or to gather intelligence. It would be a new twist on her character.
Bran Stark could also be the main character. His new powers as the Three - Eyed Raven give him a whole new perspective. He could be the one to guide Westeros into a new era. He could use his knowledge of the past and his ability to see things that others can't to make decisions that would shape the future of the Seven Kingdoms.
A Skagosian outcast. He could have been banished from his tribe for some reason, like not following their brutal traditions. This character would be interesting as he would be an outsider even in his own land at first, and his journey to either regain his place or find a new one could be full of adventure and self - discovery.
Melisandre could be a main character if you consider her as a kind of warlock. She has her strange powers, like seeing the future in the flames. You could write a fanfiction exploring her past, how she became a red priestess and gained her powers, and her further adventures in Westeros, perhaps with her using her powers in different ways than in the original series.
Arya Stark would be a great choice. You could write about her using her assassin skills to target key military leaders during the war. For example, she could infiltrate enemy camps disguised as someone else and take out important commanders, which would have a huge impact on the battles.