Best part of the Great Wall

Hello,

Would really appreciate it if someone can give me some advice about where to visit the Great Wall? We can unfortunately only go on a weekend (Sat or Sund) and being summer holidays I realize that it will be crowded everywhere. I do not want to go to the Badaling Great Wall, rather a little further away and preferably not so well-renovated! Also, one of the persons in our group is not a strong walker so rather not a very challenging area. Is it best to go with an organized tour or with a private "operator"? Any info and suggestions will be welcome! Thanks
Etienne