I sometimes think stacking bales is an art form.
We stack our bales outside using a bale wagon (sometimes called stackliner or bale picker) and end up with a flat topped rectangular shaped stack. We double tarp it and put straps over top the tarps. The tarps to keep rain and snow out; the straps to keep the wind from getting under the tarps and lifting them up like a sail -- once that happens then the grommets and strings get ripped out and the tarp ends up wrecked.
For hand stacking outside, I was taught the following: First row or bottom row of bales goes one way (eg east west direction) then second row goes in opposite direction (eg north south) then third row goes back to original direction and so on. The purpose of this method is to keep the stack tight (to keep rain/snow out) and stable (so it doesn't fall over). Also the bottom row of bales are placed on their edge side to minimize the amount of hay contacting the ground and reducing mold. To finish the stack, you can go the flat top route (in other words just stop when you've gone as high as you want) or you can stagger the bales to make a peak effect like the shape of the roof of a house (that takes about three or four rows; this method is supposed to help shed rain/snow easier but it's been my experience you loose more hay that way unless you tarp).
With regard to mugginess (and since you said you're not really in a high humidity area), if your bales are dry
(this is such an important word in the hay bale world) when you stack and tarp them they should survive the occasional day of damper air.
Let me know if anything needs further explanation.