Maybe Ron Weasley. Imagine a fanfiction where Ron, after getting married, has triplets. Given his humorous and sometimes clumsy nature, it would be really fun to see how he and his wife deal with three little ones. He could pass on his love for food and his loyalty to his children in a really endearing way.
Ron and Hermione could be main characters. They are Harry and Ginny's closest friends. Hermione might offer her vast knowledge of magic to help with any problems the baby has, like if there are some strange magical symptoms. Ron could be there for comical relief, making jokes about how Harry has become a proper family man now.
They would become more protective of each other. With a baby in the picture, their love would be deeper as they are now a family. Harry, who has always been a bit of a lone hero, would be more cautious in his actions as he has a family to think about. Ginny, on the other hand, would be more nurturing towards Harry as well as the baby.
The triplets themselves are usually the main characters. They could be given names like James, Lily, and Sirius as a nod to the original series' characters. Often, they'll have traits that set them apart, like one being extremely intelligent, another very brave, and the third having a heart of gold.
Well, obviously Harry and Ginny are the main characters as the title implies. They are the parents of the twins. Their relationship and how they raise their children are likely to be important aspects of the story.
It could be a story about the baby's special abilities. Since Harry and Ginny are both powerful wizards, their baby might inherit some extraordinary magic. The fanfiction could explore how they discover and help the baby develop these powers, like the baby showing signs of being able to communicate with magical creatures at a very young age.
Ginny might support Harry by simply being there for him. In the face of everyone else turning their backs, her presence can be a great comfort. For example, she could sit with him at meals when no one else will.
One possible reason could be miscommunication. Maybe Ginny feels neglected by Harry because he's so caught up in his own heroic deeds and doesn't pay enough attention to her. So she might seek comfort or excitement elsewhere.