I love my .22 Marlin 60. Friend had a Savage Mark II bolt action that was also great and is on my list.
So far as handguns, I tried pretty much every one that Freestate offered as a rental and settled on the Beretta Neos as my "ideal .22 handgun." It's gonna be a while before I can afford one though.
What I liked about it was that it was very easy to load the magazine into the gun. I really struggled to load the mags in the others I tried, the worst of which was the Ruger Mark III. The Browning Buckmark wasn't much better for me. Love me the Neos!
I have taken a few friends shooting who've never shot before and we always start with the .22lr rifle, followed by a .22lr handgun. We then move to shooting a .38sp revolver, which is a manageable amount of recoil for most of us (all female, btw)
Seems to be a lot of complaints about the sight screws.
The rear site screws had a mind of their own. They were constantly backing out and falling to the floor.
I finally mounted a red dot to the gun.
Baretta appears to make fine firearms with the exception of the Neo. Stay away from this gun."