You can spend money on one of the youth bolt actions - my youngest had a Savage Cricket (which I really like the peep sights - the rifle is just a little small for a grown man to shoot), but I think you'll get a year or 2 out of it.
If I had it to do over again, I'd have gotten a 10/22 - you can have 3 or 4 of those and not have "too many".
Savage Mark II is a very accurate bolt .22 right out of the box. They are lightweight, fullsize and inexpensive.
Got my son his at age 9, and even at that age he didn't have any difficulty shooting it.