Everyone should own a Smith & Wesson Model 617 .22 LR Revolver. That's a given. I have probably shot more rounds through my 617 than all my other handguns combined. It is one of the very best training pistols because it has an excellent (single-action) trigger, excellent sights, and superb accuracy. A 6" model can put all 10 shots in one ragged hole at 10 yards -- easy.
Model 617 10-shot 6" barrel
Model 617 10-shot 4" barrel
Next choice? I'll take a nice .44 magnum, loaded to .44 special velocities. Korth makes superb revolvers. Rugers have a comfortable grip. But again, the S&W is probably the best bang for the buck if reliability and excellent accuracy are top on your list. I've owned 5 Rugers wheelguns. Three had to go back to the factory for various issues.
Special mention: Colt Python -- I haven't shot the new version. But I did shoot a friend's classic Blued Python from the 70s. Great balance, great accuracy, smooooooth cycling and the best from-the-factory trigger I've ever tried. There is a reason Pythons are appreciating assets. Trivia (from Wikipedia): From the 1970s each Python revolver was boresighted at the factory with a laser; the first mass-produced revolver for which this was done.