What masonry anchor should I use to install both window boxes and shutters into brick?
Tapcons &lt;(Stack Exchange discussion) will do the trick. Just use enough of the right ones and some washers. Do not use plastic anything. Personally, they're my favorite and I dread making the holes for these, wedge anchors, when I need something to be structural. 





Recently I've begun using these, Wedge Bolts instead, where something better than a Tapcon is necessary: (all fasteners shown require a hammer-drill and a masonry bit to drill the hole, and I highly recommend using an impact gun to drive them)