I'm with Suzanne that it sounds like you are building a deck for a hot tub or something like a fort. 2by6 or 2by8's should be enough. The floor joists supporting your whole house are probably 2by12 or sometimes less. One or two 5/16" or 3/8" lag bolts at each stud would be plenty for your ledger board(if you put one, then alternate the vertical spacing towards the top and then the bottom). I don't work with stucco but put your board up first and start lag screwing it in a few places. If it doesn't compress or break, then you are ok, and if it does then draw the outline of the board so you know where to cut. Either way you will need some metal flashing and caulk it real good. I can't argue with John's posts so you have a choice.