My daughter and I are both training in Karate. We started when she was five and now she is 9. I am now testing for my Black Belt in August and she will be a Red Belt. She is on track to be Black Belt by age 11. I consider martial arts to be a lifelong activity. I am 50 and have no intention of stopping my training after obtaining 1st degree black belt.
I have spent a total of eight years training in Karate/Tae Kwon Do and I also taught a kid's class for two years. I have seen amazing results for people of all ages, all levels of physical ability, and all personalities. Marial arts, taught by competent instructors, does teach focus, discipline, self-confidence, along with physical strength and flexibility. The parent needs to be committed, also. We typically each attend two classes per week.
Any martial arts school should allow you to observe classes before committing. You should feel comfortable with the instructors and how they interact with the children. In any class there should be serious work time, and some fun. The instructor should be able to keep a class of kids focused without using any physical force or intimidation. Sparring should be about learning proper technique, not hitting hard. They should stress that none of what they learn is to be used on siblings or classmates, but only in class and for self-defense.
Most school will allow a trial period, so that you can decide if it is right for your child. Cost will vary by school. Be sure to ask what is included/not included. Some schools wrap everything up in a monthly fee, others have separate charges for each belt test, for example. Tournaments should be optional.