For youngsters I like the medicine ball. It is energetic and it is fun. I think you can start as soon as they have the motor skills.
Start by teaching them to "pass" a basket ball. After they are good at that (and can reliably catch the ball) move up to a light weight medicine ball. The kids like trying to knock each other over with the ball and it can be a very vigorous exercise. The risk is a ball hitting the face--so approach this slowly. It can work the shoulders, biceps, and triceps depending upon the nature of the toss (overhand, underhand, straight thrust).
Frisbee, and ball toss games are good exercise and can be done as soon as they are interested.
Until the joints are fully developed I think weight lifting should be to a minimum. This is repeating something I've heard over the years. I don't think there is any science to back this up. But in the absence of science to say it is safe, I repeat the caution.
I think running (in play situations, not road running) and sit ups are fine.
I think some lifting exercises do not stress the joints and I think they can be performed at a younger age (in moderation). Pull downs, rows, curls, upright rows all seem like exercises that would not stress the joints (specifically damage the cartilage). But again, no science on either side of the board.
But my favorite is any non-contact sports. (Basketball is my my categorization, a contact sport).