Horse back riding really helped train me, the non-sporty, for driving a car, more so than bicycling... actually a lot in common in terms of practice with coordinating hands and feet and thinking ahead. And fun so one doesn't realize it's exercise.

Not sure what age kids typically start, I'll toss out rowing as a possibility for a competitive group sport down the road. I never did well with team sports, never quick enough or fast enough or enough stamina to run around for an entire game of anything. But then in college I did rowing. Unless you are the front rower in the boat you don't need any particular skills in order to be a beginning rower ... just follow the leader, pull on the oars and enjoy the feeling of going superfast through the water. So one can feel some success without much instruction. Races are mercifully short. Spotty geographically where it's available. I loved having the feeling of being part of a team.