well if you want to make a stopmotion puppet your going to need atleast a wire frame armature for it to move. personally if you wanted to use clay i would use it just for things like hands and the face. and then make/use clothes around the body and fill with sponge something along them lines to bulk out. if its made purely out of clay its going to get rather squished up and be a bit more difficult to move. if you want to use a polymer clay id go for super sculpey. they have even a doll like clay thats a bit more expensive.
There are also things called BJD's, or ball-joint dolls, that are very popular. And I'm pretty sure there are a lot of tutorials on how to make one of those. Basically, they are a conglomeration parts and pieces held together with a long tight string. They pose and animate well, from what I've seen, and they have a decent fan-base that provides customization for them.
I would advise to start playing with whatever clay you get your hands on. Start with something like plasticine which is to be found in almost any art shop around the world. It is easy to model, soft and you can start from there. There are several types of plastiline, depending on which country you live in. Try to search for a medium hardness one which will allow the puppet to maintain a certain shape and not deform too much. A big disadvantage to plasticine is that the colors will seep onto your hands and from there to parts of your puppet, and in short time the puppet skin will have to be scraped or remade. But for beginning in animation and doing some basic animation it will do fine.
Polymer clay is not very good for animation but can be used. Be aware that it will loose it's properties and elasticity relatively quickly (my fimo started loosing plasticity after 7 months even in it's original wrapping) and the puppet will become quite brittle.
Also there is a clay called Puppet Putty, search for it in here or on Google and apparently that clay is specifically designed for animation. I saw some demos with it and it looked promising.
In any situation, you will require an armature that will support the puppet. I follow SugarCharm for her tutorials in designing very small items and furniture from coffee stirrers and other materials but even at that size you will need an armature in order to animate.
Thanks for the shout out, Iulian! Puppet Putty needs to be slightly warm to bend, but just touching it for a few seconds will do that. It is very responsive to the warmth of your hands, warm lighting, and any heat source in your room or workspace.
It's not traditional modeling clay or polymer clay, but somewhere in between the two with an emphasis on a light weight, non-toxic ingredients, ability to be smoothed by hand, and bright colors with minimal transfer to your fingers or other colors.
Here are some demonstrations of it in action:
Is is available in the Stop Motion Store in two hardnesses: The square package is the Firm, and the tube-like pack is the Soft. In the 3 years I've been making it, there has never been a request for a softer or harder grade, probably due to the fact that its consistency and other properties change depending on how warm it is (for example, if you melt it in a double boiler, it will pour like milk and if you freeze it, it can be carved). There is also an untinted version which is intended to be mixed with other brands of clay at 30-50% by weight to improve their working properties.
As far as Marc and I know, this is the only clay that was designed by a clay animator, so there are very specific things you can do with it that other clay can not do (like walk a puppet).