clay

What you want to do is us a double boiler and melt down your clay until it is a liquid. From there you can dip your armature into it to coat the entire thing. You can do this several times until the clay is thick. That's the best way to do it. There are tutorials in the store if you want to see examples. Particularly the puppet sculpting tutorial here:

www.stopmotionstore.com/index.php?main_page=index&cPath=1

I also have a free playlist in the tutorial section of this page of me creating a blue monster puppet. I go over most of the techniques there:

animateclay.com/index.php/articles/9-beg...ay-9x-video-playlist

Either of those should get you on the right track. If you do end up making your puppet make sure to share a picture or two. I'd love to see how it turns out.

It really depends. I like to melt my clay to the armature which causes it to be a bit stiff once it cools.

Technically you can harden the clay by cooling it down in a freezer for a while. However it will get soft once it heats up again. Another way to do it is to melt the clay to the armature. When this clay cools it does become slightly harder until you knead it in your hands a lot. If you want hard parts you might consider sculpting the forearms, upper arms, lower legs and upper legs in polymer clay you bake. Then add soft clay where the joints are so they can bend. That is a bit tricky to do but has been done by some studios.