Teach him at home. I taught Bethia self defence from a very early age. I taught her how to punch kick elbow and knee with power and technique. As for the grappling side of it rough house with him so he gets strong but dont hyper extend joints for many years
Ive done many years various martial arts full contact kickboxing and freestyle as well as a sports kung fu and a traditional style kung fu. IME if your child will listen learn and not mess around take him to a sports style of any kung fu, karate or TKD as this will teach him disapline to start and will give me a start on his technique. Move him on to other styles as he gets older but keep him out of full contact till he is an adult.Mixing martial arts to develope your own style is what I always recommend
Ground work is great and works well in UFC but if you are in a street fight and your opponant has his mates around you need to stay on your feet