Why drill into mortar vs. the brick/stone for the bracket hole? If a hole is drilled into the brick, the brick may split when the bolt is tightened into the lag shield. Besides, if you ever wanted to remove the bolt, it is a lot easier to fill a mortar hole than a hole into brick or stone.
Which mortar joint? Usually it is the second horizontal 2nd mortar joint below the sill. If that is still not enough clearance, but you do not wish to have more than 1 ½” between the bottom of the sill and the top of the box, use a vertical mortar joint. This is more difficult to make sure all holes are level, but will keep your box closer to the sill.
What kind of drill do I need? An electric hammer drill will make the job easier. They rent inexpensively.
What size drill will I need? A 5/8" concrete drill bit.
Caulk the hole before inserting anything. After drilling the holes, fill them half way with masonry repair caulking using a standard caulking gun.
Proper lag shield orientation. Insert the lag shield so the halves line up with the bricks. This will allow the halves of the shield to spread up against the bricks or stones. That is far better than “pushing” against the softer, more crumbly mortar. Sometimes it may take a hammer to tap the lag shield into the hole.