If you have a centerfire pistol, then I would recommend getting a .22 conversion kit. It would be a cash and carry deal or you could order online. No 3 trips to HPD for the long wait. You get the the same feel and trigger pull of your big gun with the ammo cost of a .22.
If you feel the need for another handgun, the best guns for accuracy is the S&W 41, Hammerli 208, Walther SSP/GSPs, and the Morini competition pistols at the steep prices.
Good accuracy pistols are the Ruger MKIII or 45/22, Browning Challengers, Beretta Neos, S&W 22A, HIgh Standard Citation and Trophy models.
Typical looking guns are less accurate, but are more compact and handier.
It all depends on what you plan to use it for.
I personally shoot a Ruger MKII Bull Barrel with a Volquartsen trigger kit and extended mag release for bulleye competition.
My Ruger SP101 .22 revolver with 4" barrel is my plinker/trainer and practice gun for my SP101 in 357Mag
My North American Arms Mini revolver in .22 is my good luck charm.
I also have a Kimber .22 conversion for my 1911 and a Ciener ,22 conversion for my Beretta 92F.