For a fast and relatively strong bond from male/wall bracket to wall we can recommend the Tapcon. However, you will need to pre-drill. Also note that while you can use the Tapcon on the aluminum bracket on brick, it's usually used in fireplace mantels, which are heavy enough that you should instead be using the steel bracket in most cases. These come in a variety of sizes. Please ask your local hardware store for more info. The Tapcon #10 is the biggest possible screw you should use when working with the aluminum bracket (any larger and the size of the screw's head will interfere with the female bracket's inner ledge when connecting the male and female brackets)
Also, remember that you need to drill the top hole of the male bracket on the dyeline exactly on the line, since if you are too low, the inner ledge of the female bracket will hit the head of the screw resulting in an inability to properly connect the two brackets.
For a better bond, use an expansion bolt. Here you must pre-drill a hole as well. These come in a variety of sizes and they may be used in grout line.
For the best bond use a real threaded rod in combination with a nut and washer. You need to pre-drill the corresponding size hole and epoxy the rod into it.
We like the Hilti 2 component epoxy. For small jobs use the 1 cartage using a regular caulking gun. For bigger jobs there is a bigger gun that is helpful.
All these bolts, nuts and rods come in variety of sizes and are usually NOT used for the aluminum bracket, but mostly for the Steel Bracket.