In addition to the properties Brian and Jack recommended, I would also suggest air dried. It will be a little less brittle than kiln dried stock. My first choice among commonly available species is hickory and second is ash.
You've heard, I'm sure, of a "square peg in a round hole?" Square pegs have less tendency to work their way out of the joint, especially if used without glue, but there are tradeoffs: They are more likely to split the mortise or the tenon, and therefore require more skill to size, shape and install successfully.