I use my drill press with it's locking stop on the quill to prevent drilling into the bore. With the barrel clamped to the table I bring the drill bit down 'til it touches the barrel and then run the locking nuts down. Having determined how deeply into the barrel I wish to drill, I find a drill bit of corresponding diameter and place it between the nut and bottom of the quill stop and lock the nuts. Now, as long as the table is locked, there is no way you can drill deeper than what you have set up.
When I use staples, I like using the staples sold by TOW. They are castings and I bought a whack of them when they first came out years ago. They are consistent and TOW's double punch matches them perfectly. I do not use TOW's set though. I have two of those, and both have pieces missing from around the bottom. Also, those sets move too much metal at once and I feel one is more likely to dimple the bore with the heavy hammer you need to move that much steel all at once. I made a set out of a nail set, simply grinding a bit of a flat on one side to slide up against the staple, then a single whack with a ball peen hammer squashes barrel steel down into the hole on top of the staple's foot. I usually use three strikes forming a cloverleaf around the staple's foot and that so far, has worked very well.
But I use a dovetailed barrel tenon just as frequently. I make my own out of .032" sheet steel or brass.
Here's a picture of a staple set into a .40 cal Rice barrel.