The sides need to be at least 2" tall to clear the stove knobs & grates. I found some wood at the hardware store that was the right width and 1/2" thick, and I just cut them to size and glued and screwed them together. It fits tightly around the stove so it won't slide around while driving. I was originally going to just attach 4 corner legs (made out of dowel) to a piece of plywood, but this design is more secure while driving.
For the top I used white board material. It isn't very thick or strong, but it's pretty well supported and should be strong enough, and it looks good and should be easy to clean. We might not want to put the ice maker on it, though. Some thicker plywood would be stronger, and if this doesn't hold up I'll swap the top for something stronger.