I start any new shooter out with a 22 revolver, then a 32 revolver firing progressively heavier loads 32L, 32acp, 32 H&R. If they get past their comfort level, they just keep practicing with what they are comfortable with. If they can shoot 32 H&R comfortably, then I ask if they want to try a 4" 38 special. This is how I prefer to teach any man, woman, or child.
22 rifles are good, too. But a lot of rifles and shotguns can make the new shooter get a sore shoulder. Hundguns just make their hands move. If they are real gung ho, or preferably on a second session, I have them start trying semi-autos: 22, 32acp, then 380 and so on, whatever they're comfortable with.
I prefer the completely obvious functions of a revolver for a new shooter. We can both look at it and immediately see if there are rounds in it or not. I frankly feel safer that way. It works the same as their cap gun they had when they were six years old. And a revolver doesn't have a slide that can whack the new shooter's finger or thumb. Getting bruised on the shoulder by a 30-06 or getting their thumb bloodied by a hard metal slide does not give a new shooter a pleasant introduction to firearms. Nor does shooting a firearm that has too much recoil and makes them flinch.
I have taught maybe a dozen people to shoot over the years, and my methods have been effective.
After a few sessions they will have a pretty good idea of what sort of handgun they might want to purchase. If asked, I generally suggest a 38 special revolver if they are ccomfortable with that, and maybe a similar 22 revolver for practice or plinking.
Just my 2¢.