Spray foam insulation: Open or closed cell?

A customer is working on his residence and would like to insulate using either open or closed cell spray foam. He's done a fair amount of research but wants to take any necessary precautions to insure any insulation will not contribute to any deterioration of the masonry walls or the embedded joists.

The building exterior is double Wythe load bearing brick wall with a stucco exterior supporting wood joists (the interior framing is post and beam and some fairly large beams are supported by the wall).

Because of the stucco he cannot assess any water damage to the exterior brick but there is evidence of water damage to the interior at some locations (the causes to this water damage have all been addressed). The home is a corner property with 3 exposed walls to the East, West, and south (largest wall) and a shared party wall to the north.