Sorry Old Grump...I have to disagree on ammo.
Jackman,
22's can be very picky about the ammo they like. Years ago I tested all of my 22's with all the different 22 ammo that I could find.
My testing showed a few things of interest. All (about 12 at the time) of my rifles shot certain ammo real well and shot terrible with other ammo. They all did poorly accuracy wise with the Hi velocity stuff like Thunderbolts. They all liked certain standard and target ammo, but they had had their favorites that they shot their best groups with. One exception was my 1939 Remington 513T, it shot almost any ammo good. And the oddest thing was the two Remington 541T's each liked different ammo. ???
The only way to get the most accuracy is to buy a box of all the 22 ammo that you can find and shoot it. Your rifle will show you what it likes.
As far as your son and his shooting...
Forget the 100 yard range for now. Start him close, 25 yards is a good distance to start a new shooter. Let him master the 25 yard range first then move to 50 yards. There's a lot of info online about proper shooting setup and techniques. Have him read and study that a bit too, it will help. Breathing, grip, trigger release, sight picture and so on.
It takes time and practice. I shot for my high school rifle team back in the early '70's and that was a real help for me, I learned a lot. Shooting all the positions and not just from a bench is a good thing. Too bad that is a thing of the past.
And don't worry about cleaning the bore a lot, my 22's shoot best dirty. I clean mine only when their accuracy falls off and that can be after many thousands of rounds. Then it takes some fouling for it to come back. I used to have a hard time with this because I like all of my guns clean inside and out.
I think you are correct for having him use open sights first. Too many today start with a scope and never master open sights. My dad taught me with open sights and a single shot, but good rimfire scopes were rare back then. The single shot taught me to be accurate when we went hunting. My brother bought his son a 1022 with a scope, that kid is a terrible shot and depends too much on blasting away...and still misses.
I taught my daughter to shoot and really enjoy watching her outshoot her husband when we go shooting. But he doesn't enjoy that very much.
Good luck, and enjoy your time with your son...they grow up real fast.
Here's what a good 22 rifle with ammo it likes can do at 50 yards. It will shoot almost as well at 100 but I don't have any pictures, just this target when I added the scope and zeroed it in at 50. The bottom two are sight in, top two were shot last. It likes Wolf MT ammo.