Answer: If the mirror has wire for hanging across the back, use hook-style picture hangers with Wall-Dog screws, which hold well in brick.
Or, if your mirror has a wooden frame, use a cleat-style picture hanger – a two-part type where a bracket attached to the back of the mirror slips over a mating section attached to the wall – with the same type of screws.
If either option would work, choose the cleat: The mirror will never shift out of level.
The hanger rating is just part of the equation. The screws also matter.
You don't need to drill a pilot hole to drive the screws into a wooden frame, but you will need to pre-drill in the brick, using a three-sixteenths-inch carbide-tip masonry bit. Use a hammer drill, which you can rent.