If the child of Han and Leia was in his/her mid twenties, the story could pick up pretty much where RotJ left off, assuming that the child was already a good pilot and a fully trained Jedi. That way we wouldn't have to retread the "seduction of the Dark Side" story, and have it focus on something bigger than that. For example, if he/she had gained so much power that he/she had godlike abilities, the story could be about the struggle to use them responsibly and for the good of the galaxy instead of using them to save friends. Or it could do what the prequels tried to do, such as make a political thriller with the goal being an ethical galactic government. Or it could introduce an enemy that simply cannot be defeated through the exploitation of an easily accessible structural weakness.

As for the cast of characters, there are literally dozens of well known archetypes that haven't been used in Star Wars. Heck, we haven't even had a scientist as a major character in Star Wars, and Star Wars is SCIENCE fantasy. We could have a noble character who has a tortured and hidden past, a teacher who knows the history of the Old Republic and who teaches our hero about how to structure a lasting democracy, a mechanical being who nevertheless uses the Force, an archaeologist who discovers the buried secrets of the first Jedi, or even a Celestial, a being who isn't particularly interested in the wars of the galaxy yet has terrible power. New characters shouldn't be a problem. I'd say the worst option would be to simply recycle what has already been done simply because people liked it thirty years ago.