I think this is a great question, but I also think the answer hinges on allot of factors. The ages, maturity level, and physical abilities alone might dictate the best answer.
I taught my own kids with slingshots, air guns, and THEN 22s...but the mistake I see lots of parents (=fathers) make is the way they introduce kids to airguns. By that I mean, comments like; "we'll let you start with this and when you're good with it, THEN I'll get you a 'real' gun". If you down-play the value of airguns, kids will never see their value...and will lose interest fast. Another mistake I see is starting kids with fussy, CO2-fed..or otherwise problematic types of airguns that fail easily and/or are difficult to use. Nothing puts a kid off faster than a gun that is hard to use, that they never hit anything with, that is so fussy that YOU don't even want to take it out to help with, etc. I mean..show a kid a wall full of airguns and they'll be drawn to the ones that are black/scary/realistic, etc. They're often the poorest choice.
If you're in a Googling mood..my first airgun was a Chinese model 61 that was in a closet full of guns we found when my grandfather died. I still have it. After that, a Crosman 1377 with a Crosman 1399 shoulder stock. Still have it, and it still works. (some 33 years later) I also bought...maybe 22 years ago..a Webley Tempest air pistol. That thing was, and still is a gem. Set me back a whopping $165, which to me was allot at the time. Some others came and went, but about a month ago..I bought a Diana 24 in 22. A non-PAL-rated spring piston air rifle shooting about 430 fps. It'll be tested on barn pigeons in the coming weeks. I still have a fondness for airguns, but very few of them are well-suited to young/small-framed shooters. The only ones that are (like a Daisy "Buck" bb gun)...even an experienced adult shooter would be hard pressed to hit an empty pop-can @ 30' with the thing. Even half-decent airguns are mostly the domain of kids about 8-10 years old..or older. A great site to check out is D&L Airguns in BC. I've bought a few things from them over the years. If you want specific make/model suggestions, let me know the ages of the kids..your budget...and maybe I can offer some ideas!
All my kids are teenagers now, and all very much adult-sized. They love rimfires, specifically scoped..bolt-action 22s. I've got that covered-off for sure. Most people default to semis thinking flying brass will be a bigger thrill. That simply hasn't been the case with my kids, my nieces/nephews. They bore of semis first, and gravitate towards guns they can hit things with. If your kids are small-framed or very young, the Savage Rascal is a superb choice if you want to "go 22" first. My kids have outgrown ours, but have so much fondness for it that they won't let me sell it. There are a number of youth-sized 22s out there, but Savage really got this rifle right in my opinion. I added an EGW rail (they make one for the Rascal
) and an older, fixed-power Bushnell Scopechief. My kids used to love shooting that prone, with a bipod, picking-off small pcs. of clay pigeons. Lots of low-power, quiet ammo options if you're so inclined. (CCI "Quiet-22" for example)
Good luck with whatever you choose, and remember "eyes and ears" with young shooters, every time.