Lessee: Where to start!
I like a bolt-action .22 for a learner's rifle for several reasons. One is the inhibiting of "spray and pray" rapid fire shooting that serves but to turn money into noise. One learns a certain amount of self-discipline about sight alignment and coordination with pulling the trigger.
So, first get skilled with iron sights.
I'd select a rifle that was already drilled and tapped for conventional scope mounts. Not one of these which are only suitable for what are called ".22 scopes" of some 5/8" diameter--which to me aren't much good.
For rifles with which one would rarely shoot beyond 100 or 200 yards, it's my opinion that for other than really fine-control target shooting, a four-power fixed-lens scope works quite well. I've used the old Weaver K4s for decades.
Sighting in is generally no big deal. Remove the bolt and set the rifle on some sort of rest (I've used books and towels, all set up on the dining table) and look through the barrel at something off at a distance. (a car's door handle, a neighbor's window, an electric transformer on a pole) Adjust the scope until as near as you can tell, the crosshairs and the center of that little dab of daylight are together.
At the range, start off sorta up close. I like 20 to 25 yards, just to make sure I'm on the paper from the git-go. My preference in zeroing a .22 rimfire is for dead-on at 75 yards.
None of the above is absolute Gospel, but it's close enough to reality, I guess.