I can't dispute anything anyone has said here, except to say a 22 LR is a lot better than a lot of people give it credit for being. I had an uncle who was killed by someone using, "just a 22," and a friend who was shot in the arm with a 22 during a mugging told me, "It hurt like HELL." Not my first choice, but a lot better than crying and begging "Please don't hurt me."
I don't know how many 22's I've owned over the years. Smith & Wesson and Dan Wesson D/A revolvers, Colt and Ruger Single-Action revolvers, Ruger auto's, and a couple of almost unknown brands. They all worked pretty well. I don't recall any of them being particularly fussy about ammo, nor do I remember any ammo having a lot of duds (I've shot Federal bulk pack for so many years, I don't remember anything else really.) I did have trouble with a Ruger MK III jamming once, but a shot of WD-40 got it right back in the game. Made a note to myself to clean/oil it more than once a year.
These days I'm down to just a couple of 22's. Both are Smith & Wesson 22 Combat Masterpieces. Maybe more money than you'd want to spend, but on the other hand, a gun for your kids to show off to their grandkids.
Totally "show off" pictures.
1954, 22 Combat Masterpiece
Model 18-4, probably from around 1980 or so, but I've never bothered to look it up.
Only two things I've ever even heard of as a complaint about them, other than the cost. First, they're only six rounds. Get a speed-loader and practice with it. And secondly they suffer from hard extraction, but I've never seen one I couldn't get to eject empties with ease by simply using small patches cut from a lead wipe away cloth to clean the charge holes. I've never tried it with any other 22, but I suspect it would help with any that seem to have an extraction problem.
If I had to have a semi for the stated purposes, I think I'd choose a Bersa Firestorm/Thunder. Small size, light weight, fairly inexpensive, reasonable capacity, spare magazines aren't cheap, but you can find them, reasonably accurate for what you'll be asking them to do. This one is a 380, but the 22 looks just like it.
You do not have to get purple/pink. It is available in other colors including black, but when Mama wanted a purple gun, she got a purple gun.