With todays bows, buying one that he can/will use in the future is not as important as one he can have fun with.
I have 3 kids, 11, 7, and 4, all have been carrying a bow since they were old enough to walk with me, shooting at whatever safe target they want (parent approved)
3D events are a family affair, really helps when there are other kids doing the same thing.
I am a traditional archer and have a couple fiberglass kids bows they started with, then an 11# longbow, an 18# longbow, a 20# recurve, a 30# recurve, and a couple 40#'s
best way (in my opinion) is to consider eye dominance, it is easier to teach them how to shoot accurately (more fun) when it is natural to see the target, point and release..
Your child will have more fun if they hit what they want.
practice makes it a habit, and familiarity will make it comfortable, so right/left hand is not that important when starting out. comfort comes from repetition and practice.
It does not matter how much you pay for the equipment, the largest investment (and payoff) is the good times and memories you have while shooting together.
another bow consideration is, what kind do you have ? as your child's desire is to imitate you.