I've used gasket rubber, as mentioned available at major hardware stores, and it is not inordinately expensive. I am fortunate to work in a factory where we manufacture camera straps from neoprene, so occasionally I get some scraps. 3 mil is better than 6 mil, although both work well.
If you want top-quality hard plastic go to a sign shop and ask for "sintra". You can get it in thin sheets, and they may even have some scraps they'd give you or sell to you cheaply. The corrugated plastic mentioned above (coroplast) is a bit thick for my liking, unless I'm making a very large character, altough it is quite durable.
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