I used 24mm birch plywood. This is way thicker then needed, 16mm would be fine as well. But I got it for free.
For all connections I used stair bolts with sleeve nuts (countersunk head). I have attached a Sketchup file so you can check the exact positions for them. Be careful finding the right size of the bolts and nuts, depending of the material thickness you are going to use.
After you have cut out all elements and drilled all the essential holes sand down all surfaces starting from rough to fine sandpaper, before putting everything together.
After everything is assembled you should sand down all the edges as much as you like and treat the whole chair with good wood oil (hygienic quality since the kids will eat directly from the table all the time.
enjoy building and using it!