Some day I will have a rechargeable DeWalt like ti94's dad has (it tore right through a steel cabinet with a 2" hole-saw bit!), but for now, my 5-amp corded Craftsman is my best buddy.
Most corded drills will work just fine - they tend to have more power than rechargeable anyway.
Also, Patrick T makes a good point about offsetting from the wall. I'm doing this for my garage really soon(not a brick wall) and pretty much building a (hollywood) flat (http://en.wikipedia.org/wiki/Flats_(theatre)) and hanging it on hooks.
I have had no trouble going through regular construction brick with any random driver, you just have to go slow and be patient. Have spare bits. There are harder brick variants that are not friendly at all, then you go into the mortar. Depending on what you will be mounting on the board, spacing it out from the wall is key. We mounted one once by sinking strips of 1x2 into the wall then the board to the 1x2s.
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Also, Patrick T makes a good point about offsetting from the wall. I'm doing this for my garage really soon(not a brick wall) and pretty much building a (hollywood) flat (http://en.wikipedia.org/wiki/Flats_(theatre)) and hanging it on hooks.
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