I have drilled and tapped quite a few firearms over the years and here are my thoughts on the subject at hand.
1) I agree a nail set is not the proper tool. A center punch is the proper tool.
2) A set of center drill can be purchased on the cheap and does a great job of spoting the hole, without the chance of the bit bending or walking.
But, I don't use either a center punch or a center drill most of the time for sight work . Here is how I do it.
1) Using a machinest clamp, clap the sight base on the firearm in the place it goes.
2) Cllamp the firearm, with clamped based in a good machinest vise on the drill press table.
3) Select a drill bit that is just a slip fit in the sight screw hole and put it in the drill chuck with the shank down.
4) Position the firearm so the drill shank enters the screw hole without touching, walking or binding.
5) Turn the drill bit around with the cutting tip down and start the drill press.
6) Squirt a little cutting fluid into the screw hole in the sight base and just touch the drill bit to the metal to form a small spot. YOu don't use enough pressure to cause the drill to bend or walk, just a light touch and a spot.
7) Now install the tap drill in the cuck and drill the hole with the mount base still in place. Use lots of fluid and don't lean on the handle. Go dlow and let the tool do the work. I back the drill out a time or two to remove the chips.
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Remove the base and tap the hole. Go slow with the tap and use good fluid. I back the tap out a couple of times to clean the chips off. All you have to do is break a tap off in the hole once to learn to take you time and do it right.
9) Screw the sight base down and repeat the steps for the other hole.
Now a couple of tips.
1) Stuff the inside of the receiver under the hole with a paper towel to catch the drill metal debris. It will save you much time in cleaning the junk ouf of the action.
2) If you are taping a blind hole, drip a little candle way in the hole before taping. It will carry the small chips out.
4) A B-Square tap wrench with the floating pilot that fits in the drill chuck is worth it's price. It will put an end to broken taps and crooked holes. I have had mine for 40 years.
5) Don't forget to deburr the hole on the inside of t he receiver.
Sooner or later you will have to shorten a screw to do a proper mounting job and here is the easy, no fail way to do it.
1) Drill and tap a piece of scrap steel for various gun screw sizes.
2) Insert the screw in this gizmo with the number of threads sticking out the backside you want to remove.
3) Touch the backside to the grinder to remove the threads. Keep the screw from turning with a driver or pair of grips.
4) When you back the screw out of the gizmo, it will deburr and clean the screw.
Lots of folks try and take short cuts when drilling and taping, but often the results are hole in the rong place, canted holes, broken taps and the like. Take the time to do it right and you will never have these problems.
Oh yes... A good high speed drill bit will do for most gun work, but sooner or later you will need a carbide bit. You won't drill and tap an O3A3 action unless you spot anneal the place or use a carbide drill bit.
Das all....