I like to use the inexpensive footlockers sold by Kmart and Walmart. They have black with gold metal trim, very pro looking and now even wheels at one end to pull.
Maher Studios also sells cases for dummies http://www.maherstudios.com
Lowe's hardware stores have a nice plastic "footlocker". I believe they have a version with wheels as well. It is lighter than the wood based footlockers and not as wide, so it can be carried more easily. For local transport I actually pull my bear out of a 55 gallon yellow trash can with 10 inch (or so) wheels. The large wheels get over any curb, I can put my vent stand and backdrop curtains inside, as well as 2 or 3 other puppets. I put the tripods on top and voila! It's also a quick clean up by tossing everything into the trash can and wheeling it out. The rat would be a trash can natural as well.
I like to have the case serve as a prop as well. For example... Pull a jungle character out of a suitcase with jungle designs. Pull The Old Storyteller out of a cardboard box with "First Class Postage" all over it. "My father in law wanted to visit, so I said I would send him here first class!" Then bring out the box.
Check out pet carriers at pet stores. Add some black cloth to hide the view and you have a natural look. Perhaps a bird cage with a cloth. The point is to try to make the case look like a prop. Do that for your largest puppet and then add the smaller puppets to it for carrying.
Of course, if you fly a lot, check out the Lowe's case.
Just in case you are interested, I use a case like Steve suggests. It is a footlocker from K Mart. I modified mine by fully lining it with cabinet shelf liner. (The rubbery type) I also put some recessed handles on the sides and it made it so much easier to carry and handle. Incidently, a keyboard stand is great to sit them on during your show. They are lightweight, easy to transport, and they're pretty inexpensive. Placing your case on a stand will keep it at a good height for easy accessibility.
Wal Mart also has light weight plastic cases perfect size to carry several latex puppets..look in the automotive section where they have their truck tool boxes.