Much of the answer depends on what you plan to use for fasteners.
For this job, I would probably go with either lead anchors that can accept a 1/4" or larger fastener, or a 3/8" sleeve anchor. A mailbox gets a fair amount of abuse and you want something more than a simple Tapcon (IMO), and something that makes it easy to remove and replace the bracket when or if you eventually need to.
Drilling the holes should be pretty easy with a hammer drill and a *quality* mason bit. If you're drilling a 1/2" or larger hole (possible for some sleeve anchors) you might find that a diamond/carbide style core bit is easier than a masonry bit/hammer drill (you're removing less material with the bit with a core drill, goes faster). The issue with most cheaper core bits is they may not go deep enough, so you drill and then use a cold chisel to "pop" out the plug and continue drilling.
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