When I got interested in handguns "back in the day", the revolver was king. I started off with revolvers and for my first .22 revolver I was deciding between a Ruger Super Single Six or a S&W Model 17. I ended up buying the Smith and still have it today. Either would have served.
I'll give two general recommendations. First, that your first purchase be a .22 caliber, and second, that you buy a top quality gun. It is not only a good "starter" gun, it is one that you will never outgrow and can always appreciate. Even if you handload your centerfire ammo, the .22 long rifle ammo is less expensive.
I still appreciate a good revolver but I often recommend, for new shooters, a Ruger Mark II/Mark III or 22/45, or a Browning Buckmark. Both are reasonably priced, accurate, well made and supported in the aftermarket (holsters, sights, etc.).
About a year ago I started shooting Steel Challenge with a .22. I like the Buckmark but ended up buying a Ruger .22/45 for a couple of reasons. First, the Ruger can be dryfired without fear of damaging the chamber. In Steel Challenge the RO directs the shooter to dry fire the gun at the end of each stage (after showing clear) to confirm that the gun is empty. The Browning does not tolerate dry firing as much. Second, I needed five magazines to shoot Steel Challenge. The Ruger came with two, the Browning with only one, and the extra magazines were less expensive with the Ruger.
Good luck with your purchase.