Hi Dave,
The answer is: Whatever size trowel you need to get good coverage. How flat, or how "un-flat" your wall is plays a huge roll in this. If it was glass flat, you'd be able to burn a thin coat of mortar onto the back of those stone tiles and use a tiny notched-trowel on the wall. But if the wall is wavy, the notches would need to be larger. Typically, a 1/4" 3/8" x 1/4" for the wall is plenty...sometimes too much.
As for the thickness of the wall for cabinetry to be built, you are putting the carriage a bit in front of the horse here if it needs to be absolutely perfect. But you can accommodate by having the cabinets built with "extended stile(s)" so it can be trimmed for a perfect fit.
