Anyway, I have come across that the easiest and cheapest way to get going with semi decent stop mo puppets is make a wire armature (with plumbers epoxy for shoulder and hip reinforcement), then cover it in foam from our sofa (furniture foam). The head and hands can be done with liquid latex brushed on, you can get liquid latex at art shops.
This thread talks about
"Hollow slush cast" - that's where you make a plaster mould, pour in liquid latex and leave it stand for a while, then pour the latex back in the jar. The plaster mould absorbs water from the latex, so a layer next to the plaster starts to get thicker and is left behind when you pour the latex off. The longer you leave it the thicker it builds up. After it dries you have a hollow skin. Dust the inside with talc, peel it out, and you have a hollow puppet head. I used this for hand puppets, where I put my fingers in the upper lip and thumb in the chin and operated them like Muppets. I made the mouth open so I could squeeze it closed, but it would spring back to open.
For foam heads I sculpt the mouth barely open, because it creases in a weird way when you close the mouth a lot more than it's original position. But the foam can usually stretch open more.
Yes, you need a head armature with wires for the upper and lower jaw, and also for anything else that moves like eyebrows or animal ears. They have to attach to a block in the middle, and you need neck wires to connect to the body. You have to make sure the wires will sit in the right place in the plaster mould.