What size is this wallplug, and then what drill size (and type) would I use for brick?
Use the Black &amp; Decker drill bit for masonry. 8 mm is compatible with the 5/16" size you gauged. If you choose, for a guaranteed tight fit, use the 7 mm drill first and if the insert is too tight, go up to the 8 mm. Even if the insert slips into the hole, the little "wings" should keep it from spinning in the hole until the screw goes in far enough to swell the plastic to a tight fit.

After the hole is drilled a little extra deep, do what you can to blow the dust out, so the anchor grips the actual hole, not the dust in it.