First the 10-22 is never a bad choice.
Second the M&P 15-22 may or maynot have a safety issue but you can’t use it at an Appleseed shoot. Read up and figure that one out yourself. I’d go with 10-22 before 15-22.
There are two ways to do an AR 22 conversion. One way is to simply replace AR bcg with .22 adapter. The twist rate of an AR barrel is not correct to get high level ofaccuracy out of .22 ammo but plenty of fun for plinking. The other way is to build or buy a dedicated .22 upper for the AR. There are other threads on that already. A dedicated .22 upper is more expensive than buying a 10-22. However you get very good accuracy and you are practicing the same movements as with AR in usage.
I have both 10-22 and dedicated .22 upper for AR. I shoot the dedicated upper a lot more. When I have newbies or youngsters on range fun shoot everyone likes the AR with dedicated upper the most. Low recoil and report and high cool factor. In fact I built a second dedicated.22 upper that I use with preban lower with adjustable stock for kids.
Personally I shoot AR with dedicated upper a lot. I can do a lot of positional practice ( shooting prone, sitting, standing) while doing mag changes and practicing shooting various position with cheap .22 that translate to better center fire scores.