1/2 to 3/4" thickness is the usual for making foam puppets.  Many puppet makers use the green as LJ said....since they cover it with fabric.....however if you want to dye it then you need the get the creamy colour stuff.  Try looking up Foam in your yellow pages you might be amazed that you have a Foam shop in your neighborhood.  Good luck.

Just a thought......

Daryl H