Just a couple of points to add to the good advice about starting with
a centre drill and so on.
Firstly, stainless steel has an absolutely ferocious tendency to work
harden. If the drill rubs rather than cuts, just briefly, it will
harden, and be impossible to drill in the sizes you are interested in.
So, you need really sharp drills, and a deft touch on the feed lever
of the drill press … the drill must be cutting all the time it is
in contact with the stainless.
Secondly, remember that this stainless is tough stuff. Make life as
easy as you possibly can for the tap. That means using a lubricant
(“proper” stuff is available from engineering suppliers, but just
about any oil will help somewhat, and use it on the drill too), and
look to the size of hole you are drilling. For your application (I
assume we’re still talking body jewellery here?) where there will be
no great mechanical stress on the threads when in use, you could
a slightly larger hole than that recommended in the tables, and so
have less metal for the tap to move. – Kevin (NW England, UK)