I like my little SIG Mosquito and the Walther P22 as well. You can't beat the Ruger 512 for dependability and value.
Most all .22's are persnickety about ammo. Skip the Federal bulk packs for starters. Keep them meticulously clean.
Both the Mosquito and the P22 are ideal for smaller hands. That's a big part of their appeal, as well as the 'controls' being in the same places as their bigger sisters.
SIG has now done something kind of unusual. If you want a P220, 226, or 229 frame in .22 caliber, they are offering them and you can buy them for as little as $375 on GunBroker.
SIG got themselves a pile of very nice (99.9%+) police trade ins. Instead of flooding their market and ruining the prices of their new centerfire guns by putting these 99.9% guns on the market- they had a smart idea (and put their armorers to work in the refurb unit)
They weren't ever really selling any of the optional .22 conversion units (slide/mag/barrel), so they clapped the .22' units on the trade in frames and sent those out. Voila- a dedicated .22 cal large frame SIG.
SIG is banking on their theory that your going to want the orifinal centerfire top end, so included in every pistola is a certificate for just that. If you send SIG $399 (bypassing the dealer), the factory will mail you directly the .45/9mm/.40 top end and magazine. If you look at it from SIG's terms, they make out like bandits by selling the top ends directly as well as unloading all of the large frames without collapsing the new market. Buy that man a beer.
If you get convinced that you need a centerfire SIG, it all comes out to $800 or so with both calibers.
If you are happy with a Large Frame SIG with a .22 appetite, you're in for $375+ fees.
Additional .22 magazines? I bought 3 for $89.
They run well, but they are more prone to failures than a centerfire. It is, therefor, an excellent gun for training, this is why I also utilize a Colt Service Model ACE and a Glock fitted with an Advatage Arms .22 conversion. It teaches real life FTF drills and allows for repetitive shooting at a fraction of the cost.