First a bit of advice about shooting a handgun. It is just like the martial arts. One must perform a motion enough times to form a muscle memory that become instinctive. This includes training your breating, stance, sight picture, trigger control and followthrough. It can take thousands of times to get it right. Practice makes perfect only when it is perfect practice!
The advice about starting with a 22 is sound. Cheaper ammo equals more rounds fired. Low recoil reduces flinching to a minimum and you can actually see what effect jerking the trigger or bad breath control has. Hearing and eye protection is a must, however, even with a 22. Diagnostic targets are available that will show if you are heeling, jerking, anticipating recoil etc. and they are usefull.
As regards reccomendations the top of the line would be a Colt Officers Model Match for a revolver and either a Smith and Weson M-41 or a Colt Woodsman Match Target model for a pistol. Very expensive, hard to find, lovely to behold and objects to be cherrished. Accurate in the extreme.
Next down would be a Smith K-22 Masterpiece (6") or Colt Diamondback (4"). again hard to find and very costly.
Ruger MK-II autos and Single Six revolvers are much easier to come by but they usually have atrocious triggers out of the box and it can take a couple of thousand rounds to slick up the action, the trigger and lap the barrel.