Read this for a primer, should answer all your questions:
http://www.opticsplanet.net/how-to-choose-riflescope.html
I would start the kid on iron sights on both rifles, 10-22 and the mini14. I actually would not put a scope on the mini at all. Maybe a red dot for the mini - but see below.
Shooting with open sights is an important marksmanship skill. Pistols usually have open sights, so do many muzzleloaders and classic rifles. You want your kid to be able to pick any rifle up and shoot it, even if it is just for fun at camp or at the range. Also, the lining up of sights and target will transfer very well should you choose to start archery with a compound bow!
The red dot scope is a fun aiming device but I would reserve it for quick shot acquisition shooting, for example on a handgun, close in hunting rifle or a battle rifle. I do not think it does a whole lot more than a good set of ghost ring (peep) sights though and the ghost ring sites never run out of batteries! Look for XS ghost ring sights for the mini, if you don't like the stock iron sights.
If you buy a scope, make sure it is water proof and nitrogen filled. That way it won't fog up in the field. Lower magnification will give you better light output. I recommend a fixed mag anywhere from 2-4X for the 10-22 (after you are done with iron sights). I like the Bushnell line of scopes - you will want their top end stuff - Bushnell Elite. They are made in Japan. Can't beat them bang for the buck IMHO.
Hope this helps. Have fun!
George