I think it depends on the kind of puppet you want to make: if it's a sophisticated sock-puppet design(like Kermit, who has a flexible mouth)I'd suggest something flexible yet sturdy as the base, and attach a felt inner mouth design via spray glue, inconspicuous sewing, and the like. For other puppet types with the less flexible head, try a sturdy material that will be forgiving on your hands when you're operating with it. I used some foam board.
I hope this helps! Good luck!
Greedo