First, you can use screws or nails, but make sure they are either stainless or zinc coated. Some zinc does eventually come off, and rusting could leave rust marks. If you caulk and prime and paint over them that should work.
screws or nails??? Stainless deck screws will work fine, if that route, slightly embed them so that they barely bend the board and cause an indent, then caulk or spackle and their gone.
If nails, a good ring shank nail will work fine only if you do hit the studs on every drive, this is of course on the screws also.
Caulking, I would caulk all the overlaps for sure. Use a good 35 year silicon/latex paintable caulk. Let dry thor. before painting.
I would use a "Z" flashing above all windows and doors.