It it were my job, I would install the box in the brick so that the front of the box is flush with the brick and only the in-use cover is sticking out. The circuit should originate from the main panel. I would run a 20A branch using 12/2 WG NM cable. How it is wired will depend on where the switch will go in the circuit and how access is through the walls.
The box and receptacle must be weather resistant, and there must be an in-use cover installed on the box.