Annabeth Chase is another key character. Her intelligence and strategic thinking would be invaluable in a combined - camp scenario. She could help plan out quests or defenses against common enemies. And her relationship with Percy would also be an interesting aspect to explore, especially when faced with the different cultural norms of the Roman demigods in Camp Jupiter.
Percy Jackson is an obvious choice. His abilities and leadership skills from Camp Half - Blood would be a great addition to any story where the two camps meet. He could interact with the Roman demigods, maybe even have some friendly rivalries with the strong leaders from Camp Jupiter like Jason Grace. His loyalty to his friends and his sense of humor would also add a lot to the story.