When we say the words "self-defense" we are already lagging in the OODA loop (Observe; Orient; Decide; Act). Self-defense by definition is a reaction to an attack. The sociopath doesn't worry about self-defense--he knows what works for him historically. There may be a time when we are caught by surprise, but in the study of Injury Dynamics, our intent is to cause more injury to our antagonist than he can cause to us. This means knowing how to injure another human being and having the intent to do it. So when is an appropriate age to teach our children? There is no easy answer to that. A lot depends on the maturity of the child. The last thing you need is to be called by the school because young Jimmy throat stomped another child over a childish altercation.
While there is no easy answer, I am a proponent of getting kids involved in "martial arts" schools as early as age 4 or 5. For most children under the age of 14, martial arts schools are a place to learn athleticism, dealing with adversity, and respect for teammates and teachers. They can learn the basics like how to fall, basic throws, and some basic striking--all appropriate for the school altercation. Once they hit about 13 or 14, depending on the maturity of the child, you can start teaching them the serious nature of exacting real injury on another human being--skills for saving their life and possibly at the expense of the life of their antagonist.
For young women, high school is totally appropriate for teaching them these skills. Ask a man what he did to avoid sexual assault this week and you will be met with a blank stare. Ask a woman and the breadth of answers will surprise you. And young women represent the part of the population most at risk for assault.
In general, I find that children who are really involved in martial arts (irrespective of the style) or coached firearms training generally exhibit a maturity that makes them stand out from their peers. This short video is an exploration of the topic of kids and martial arts.
For kids, Krav is a good one, but just about anything from Tai Kwon Do, Jujitsu, Hapkido, Judo, Karate, and Silat work well. For the more serious training, Injury Dynamics/Target Focus Training and Krave Maga would be my recommendations. Good luck!