Normally when I build something for outdoor use I just cheap out and swing by the lumberyard (not the big box stores) to pick-up some PT lumber. My MIL wants me to rebuild their "trash can shed". The current one has all kinds of really nice (probably pine) quarter round and cove trim on it. It looks really nice, other than it's rotting apart. As I mentioned, I would just grab some PT and have at it, but I have a feeling that sending pieces of a PT 2x through the router table to make coves and roundovers would probably destroy the bits.
What woods are good, sturdy, and cheap for outdoor use? Keep in mind that this will be painted, so grain and the like don't really matter.
What kind of plywood is rated for outdoor use? (ie., what do I ask for at the lumber yard)