"Would like something that is well thought of but common enough to not be too pricey."

I'm not up on the commonality and prices of the K-22/Model 17, 18, 34 other modern .22 caliber models, but they are certainly well-liked. Also consider the J-frame Model 317 .22 Airlight.

Others that come to mind the in well thought of and not too pricey category include:
.38 Military & Police/Model 10.
.357 Combat Magnum/Models 19 and 66.
.38/44 Heavy Duty and Outdoorsman/Models 20 and 23.
.357 Magnum/Model 27.
.357 Highway Patrolman/Model 28.

The N-frames will be too massive for young hands to control, but you will appreciate the design and craftsmanship of early examples. I think the 1950's era pre-model Smith & Wessons are an excellent entry to collecting.

You mentioned the 642 and 686, both fine examples of modern J and K/L frame. I have a fondness for the 640-1 .357, the 629-2 and -4 Mountain Revolver/Mountain Gun, and the full lug 29 Classic from the early '90's.

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Tom in AZ
Respect the Dingbat