What type of bolt should I use to maintain a movable joint?
For neatness you could consider the use of a carriage bolt through from one side of the wood "pivot" point and then put a flat washer and a nyloc nut on from the other side. The parts look like this:

Carriage bolt - The square part under the rounded head keeps the bolt from turning in the wood.



Flat Washer - This keeps the nut from digging into the wood.



nyloc nut - This special type nut has a nylon insert that keeps the nut from loosening and spinning off the bolt.