Given your cost concerns, it seems to me that the most effective interventions would be those that he can do at home, with some outside activities added as a supplement. So, karate once a week can be more than sufficient, so long as he has an outlet for that at home that he does regularly. A punching bag, a parent to spar with, a hanging ball target, etc. For my DD, gymnastics was the activity, and we bought some foam "puzzle pieces" to place on the floor in her play room. She does this practically every day now, but the financial commitment has never been more than two lessons a week (usually just one), and we shut it down seasonally.
Ball sports can be a good way to work on several of those areas of concern all at the same time, so that simplifies things greatly: gross motor, sensorimotor, core strength, visual-spatial, and coping. That's something that anyone can play with your DS, at home or at school, apart from any formal participation. We find that of all the options available, DD's soccer league provides the best value for the dollar.
