When creating a character or a puppet it is important to have that character be able to match his persona. To accomplish this one must draw and redraw your puppet idea.
For myself I do a rough sketch of what I think I may want for the puppet keeping in mind the persona so if the puppet is supposed to be spastic and weird I would need to work that into the drawing. Usually the first drawing is half way decent. I then try and think about some ways to improve that sketch.
Once I have figured out the elements I want to change I will redraw the design. This may take several drawings to get what you want. Take your time and have fun with it.
I then create a Model Sheet once I have a final look for my puppet. This allows for me to think about the puppet in three dimensions. My model sheet usually contains a profile, 3/4 angle, and a frontal view. The model sheet can also contain some drawings of details such as hands, teeth, etc..
Once I have all that I began working on the puppet. But, that is another post.