I just went through the "which .22LR autoloader" process and ended up getting a Ruger MK III.
I wanted something that would be reliable, accurate, comfortable, and relatively inexpensive for mostly range work. I live in the city and don't see using it much outside, maybe just a few times a year. Consequently, it will go mostly from my house to the range in my range bag and not see much holser or backback time, if at all. So far I'm pretty happy with my decision, although my impression of the Browning Buckmark and Sig Trailside is that, anecdotally, they're in the same class as the Ruger.
I don't know much about the Neo, so I won't comment on it.
However, I did handle a P22 and believe that it's really a "Mini-Me" version of the P9X line and not really in the same class as the other, more full-sized .22s just mentioned. I think the P22--even the longer barreled version--is best suited to a lightweight backpack weapon that could easily be transported due to its small size and light weight. If that's your bag (sorry for the second Austin Powers reference), then the P22 is really a standout and has no equal.
But according to my research, the P22 is not a very strong competitor for target work at the range compared to other models. The P22 is not likely to be as accurate and is said to be fussy with ammunition. It does look cool, though, and it could be the best .22LR autoloader for smaller hands.
You will have to decide for yourself, though.
Good luck