It looks like you've got the "corrective" suggestion, but you need a balanced approach. If you're not already, you need to make sure you keep your kitten stimulated as well. You should show him the ways you want to play (string toys, tossing little mouse toys). Have multiple daily play sessions. If he isn't getting the playtime he wants, he's going to go out and find it by chasing people around or knocking things off tables, etc. Show him he can bite and claw the toys all he wants. When he bites or claws you (or any human), playtime is over. You get up and walk away.
Make sure you provide hiding places and things he's allowed to climb and scratch. When he scratches something he shouldn't, pick him up and take him to a scratching post he's allowed to scratch. When my cats were younger I would scratch the posts myself with my nails and put their front paws on the scratching post so they got the idea. They still occasionally scratch things they shouldn't, but a stern "hey" as a reminder and they remember their manners and stop, but they use their designated scratching posts like 90% of the time.
Good luck!