RE: New to this
I'd just go to a couple of gun stores and handle a few to see which you are most comfortable with. Probably the biggest choice you'd need to make is whether you wanted a bolt action, semi-auto, lever, or single shot.
I'd just pick a few up & see what you like the best. I have a Marlin bolt action that I really like, but that's just me.
Also, don't be afraid to get a used .22. You can usually find excellent used .22s.