We want a built-in bench in the breakfast nook, and decided that a wall-mounted would be good (and match the various other wall-mounted items we have).
To get the strength and rigidity needed, we decided to install the frame right into the wall. We cut holes into the wall on both sides and at the end of the bench (by the door). Then we installed a 4x4 on blocks in wall and attached it to the studs. We also put in two pieces of 3/4-inch plywood screwed together and attached directly to the stud.
Next, we put in 4x4 between the first 4x4 and the plywood frame. This is everything that will hold up the bench.
Then we put the drywall pieces back in and sealed them.