NOTHING BEATS A RUGER MARK II
I have two options that I own and have good opinions of. I am sure that there are many others.
Most of the the Heritage Rough Rider revolvers come with a .22lr and .22mag cylinder so you can fire either. You can usually find them for under $200 so it is a good value in my opinion. I have used ours to train my daughters to shoot pistols, and I can tell you that we all enjoy it. The finish is not the highest quality, but I keep mine very clean and have had no problems with the blued finish or barrel or cylinder.
The second is the Walther P22. This is a semi automatic pistol that I have found fun to shoot and fairly reliable for a .22lr semi auto. Mine was a little picky with ammo at first, but over time and after the break in, is more forgiving. I liked it because it also came with a threaded barrel from the factory, so when I decide to go the suppressor route, the P22 with be good to go. I picked mine up new from one of the 1500 shows for less than $300.
One thing that frustrated me previously was that the magazines only hold 10 rounds, but they load quickly and are cheap enough to get some extras.
Hope it helps. My ...
I have two bull barrel, a 5.5 inch & a 6 7/8 inch GOVERNMENTboth have adjustable sightsExcept having two Ruger Mk.II
for Ruger Mark series.