I would second what Bear Man was saying above about memory foam, it tends to be very dense and heavy. I would also stay away from eggcrate foam unless you already have some lying around and just want to experiment with it.
Many puppet builders like to use reticulated foam, which can be hard to find in small quantities in stores because it's typically used to make industrial filters. It is very light and very breathable, but the downside of reticulated foam is that it breaks down over time, usually after 10-15 years (other foams break down over time too, but not as quickly).
Project Puppet sells 16" X 36" sheets of 1/2" thick reticulated foam for $33.50 US. They also sell 4"x 4" x 8" blocks of reticulated foam for $18 US. It's expensive, but the quality is very good.
http://www.projectpuppet.com/puppet-supplies/
Foam Factory sells a reticulated foam called Dryfast Foam that comes in 1" thick sheets. A 90" x 25" sheet costs about the same as a smaller sheet from Project Puppet, but the trade off is that you have to work with a thicker sheet of foam. I haven't ordered from Foam Factory myself, but I've heard good things about them.
http://www.usafoam.com/outdoorfoam/outdoorfoam.html
Upholstery foam - or "polyfoam" - is easier to find locally and usually much cheaper. This is the stuff that couch cushions are typically made from. I believe that Joanne's sells polyfoam in its stores across the US. A cheaper source is probably Foam Factory, which sells 3/8" polyfoam sheets measuring 82" x 36" for $4.50 US online, which is a pretty good price. That might be a good material to start with.
http://www.usafoam.com/opencellfoam/poly.html
If you decide to use more expensive materials like reticulated foam, be sure to buy some cheap polyfoam too. I always mock things up in polyfoam to make sure my patterns are correct before I cut reticulated foam. Also, it's a really good idea to make your patterns first so you know how much foam you actually need.
I keep a Pinterest Board with a lot of puppet building resources that might help you. Have a look at
https://www.pinterest.com/puppetvision/puppet-building-resources/