Given that you want a snubbie (my favorite pistol), and that you're willing to buy two guns at once... I'd try and find a great 38 snub (Smith and Wesson) and a similar frame 22 but with a 4" (or even 6") barrel for the 22.
There's no reason in the world why anyone can't get good with a 2" bbl BUT if you're new to handguns, it's probably a great idea to have some really good results early on. A longer bbl 22 will allow you some early success instead of some early discouragement. Shoot and dry fire regularly and you'll get good with the little detective gun.
I don't think it's ever a waste of time or money to buy two guns of this type. For any gun, especially a pistol, the cost of your ammo will very quickly out strip the cost of the gun. Assuming you could find ammo, you could shoot that 22 a few thousand times while you shot the 38 a hundred times. That's a lot of good practice with sight picture, trigger control, flinch management, hand-eye coordination, muscle memory. Shooting just 1000 rounds in any pistol is a REALLY good start at getting REALLY good. You could do that for maybe 50 bucks in the 22, maybe 500 bucks in the 38.
A pair of Smith and Wessons, one in 38 one in 22. Add a bunch of ammo. Have a blast..
Sgt Lumpy - n0eq