Ive checked out your puppets and they are all fantastic!!
the fiberfill method, as others have said is a fantastic way to go, so even when you progress onto foam, don't let go of the fiberfill way.
when i stuff a head (which i still do in some cases even though i professionally make puppets now) i sometimes create a barrier of fabric in the head, sort of like the pillow method people are talking about, but the upper pert of the head IS the sealed pillow rather than inserting one in, i found that it worked really well and made sure the fiberfill didn't come out.
in answer to your question about thickness of foam, i use more half inch than any other thickness, it is thick enough to create shape with, but thin enough to not prevent great movement, after all when you have made the foam head, you'll probably still be covering it with fabric, which is another layer adding to the thickness, which in some cases can interfere with the movement. i use the inch thick too, but mainly for bodies and areas that need a little more rigidity, or for building up facial features.
so i would buy the half inch thickness and play around with it, maybe even print out one of the free patterns on this site and see how you get on, i think billy still has some patterns in his album somewhere, or maybe support a good cause at bashful puppets by purchasing Jon's prairie dog pattern for a few dollars (if he still sells it)

Hope this helps a little,

Ben.

1/2" foam is what I use, and, I suspect, pretty standard.

I agree... great job.

Thank you all for your encouragement and comments, we are loving it here. I really appreciate the comments on Ron the zombie puppet. He was really a project the whole family contributed to, and he really should have been named Rob..Rob Zombie...now to go work on a living dead girl.

The foam at Wal Mart (in the craft/floral dept is 1" (at least it is in the ones I frequent). 

HA!  Your zombie looks great!