A .22 like the ruger .22/45 is great for high-volume practice. I find that I shoot more carefully, taking my time with more expensive calibers, like .357 magnum. A beretta 92, a 1911, or any quality handgun, even a revolver, would make a fine first handgun. Take a look at the "what was your first gun" thread. You'll find just about everything in there.
The most important thing is learning good technique and good shooting habits. they translate to all types of firearm quite easily.
While the P22 and the sig mosquito are great guns the sight radius on the p22 and the GOD AWFUL trigger on every Sig I've EVER seen preclude me recomending them as learning guns, If I had to choose it would be the P22 with the long barrel or if you were going to pop for a trigger job the sig would be good,
All the first mentioned BIG 3 guns have long sight radius' so that's my reason for my recommendations.
if you were in the ruger frame of mind and ran across one of the old MK2 Government model I think those were about the best starter just because they were screened for accuracy and trigger pull.