Choices...
Interesting choices you offer... Among my .22 autos, I currently own all three of your selections (although my M&P is the American-made Compact). I regularly use all three, with great satisfaction and reliability. Not from the beginning, as the Umarex-made Mosquito needed minor polishing and +/- 800 rounds of break-in. Maybe an exception, but the diminutive Umarex-P-22 has been highly reliable from Day 1, the only issus being mediocre accuracy, and ammo-dependent ejections toward the shooter's face. The lack-luster overall satisfaction level had prevented me from trying the Umarex-M&P .22 (full-size) when introduced, and the early reports of dissatisfaction eased any regrets.
If you haven't had the chance to handle them yet, here's some observations to consider; the P-22 and SR-22 are really small. Great for the young or petit, still manageable for an average hand. The Mosquito is smaller than most other Sig-branded offerings, yet the grip is about "medium" sized, overall. The Smith & Wesson produced (not Umarex/'full sized') Compact is about the same grip size as their Shield.
When Smith & Wesson announced their in-house Compact with a freshly developed design, I read all I could, and found one locally. Very glad I did! Ho-hum trigger, pretty good accuracy, and exceptional reliability. Just under 2,000 rounds so far, and less than a dozen failures to feed, extract, or eject that I can recall. With all sincerity, I believe that anyone who shoots plinker-level, rimfire, auto-loading handguns will admit (at least to themselves) that that's pretty darned good.
All three of these were purchased with my young son and wife in mind, and they have ultimately turned out to be good choices. If I knew then what I know now, I could have saved some tinkering & ammo, by skipping the Mosquito. My son has grown quickly, and the extra-small grip of the P-22 no longer offers any advantage. The S&W Compact could be considered a 'trainer' for the Shield, if I had or wanted one. Overall, the Smith eats everything from cheap, cheap imported low-velocity ammo to domestic high/hyper velocity ammo, without a hitch. No break-in to speak of, this is the one I would probably suggest to someone who only wants one, and is limited to the choices you have offered.