There's nothing wrong with having a few .22 handguns, I have... lemme think... six, three revolvers, 3 semi's, and I plan to get the CP33 when they become available for under $450.
I just got a Phoenix .22 this weekend and for $120, it's the best $120 you'll ever spend and is probably the best small .22 semi auto you'll find for the money. After you understand how good a .22 pistol is, step up to something larger and holds more rounds. We're fortunate we live in the times we do as prior to a few years ago, a .22 semi auto that held more than 10 rounds was unheard of. Now we have Taurus holding 15 rds, a new Kel Tec with 17 rds, the CP33 that holds 33 rds and maybe 50 in the future.
There are bound to be some in this thread that will yammer about the Ruger Mark, Browning Buckmark, or S&W Victory being "quality" because they're steel... you don't need a steel frame .22 to be your first .22 pistol. I also don't think conversion kits are worth messing with, instead of having two guns, you just have one that shoots different calibers.
That's great for a .40 to 9mm conversion because they're so close in size all it requires is a barrel change, but the .22 is as small as it gets and is not as simple or cheap; I'd rather have a pistol built from the ground up to be a .22.
My recommendations to start are go with a Phoenix semi auto and a 6 shot Heritage with 6.5" barrel and adjustable sights:
https://gun.deals/search/apachesolr_search/753733102236
https://gun.deals/search/apachesolr_search/RR22MBS6AS
If you like these guns and want to step up to something better, the SR22, Mark's, Buckmark's, Victory, or Kel Tec's are good options depending on what your intended use is.