I'd say any of the "squirt gun" style classic .22s will work just fine. Look at the Ruger MkIII and 22/45, Browning Buck Mark, S&W 22A, Beretta Neos, and maybe an old Colt Woodsman if you can find one. The SIG-Hammerli Trailsides are also excellent pistols, as already mentioned, they're just a bit hard to find. They're all very accurate as it's difficult to screw up a fixed-barrel blowback .22 when it comes to accuracy.
As for barrel length, a longer barrel will increase velocity and make the projectile shoot flatter, and the longer sight radius will make it easier for you to make accurate shots, but it won't make the gun itself any more accurate. At the ranges you're typically firing a handgun, the slightly flatter trajectory won't make a noticeable difference, and the sight radius is irrelevant if you're using an optic.
That said I personally recommend a 5-6" Browning Buck Mark. A Contour 5.5 would make an excellent small game pistol.