For a first .22 pistol I would go with a Browning Buckmark or Ruger MK series or 22/45. Either of these guns will do you great. I personally like the Browning better but have owned all of them. They never miss a beat and will eat any ammo you feed it.
I would stay away from the Sig Mosquito and the Walther P22. Very picky about ammo if you can get them to feed at all.
Good luck with whatever you choose. Everyone should have a .22 pistol in their collection, or have 5 of them like myself