Like others have said CZ makes really nice bolt actions. CZ 455's and 457's are great but are a bit more pricey at around $600-800, but the quality shows. Henry makes the H001, at around $400-500. This lever action can shoot 22 long, 22 short and 22 long rifle so if your looking to limit the round to shorts this could be a really good pick. If you want to get something a bit cheaper then that, you can get a Canadian made Savage MK II, at around $300. All Savage rimfires are made in Lakefield Ontario. A Newer design from theirs is called the savage B22, and goes for around $400-$500. But at 10 years old, I know I'd be happy with any rifle, so I'd probably recommend the Henry or a Savage instead of something like a CZ. Or you can get a single shot I know it's not what you listed but nothing wrong with learning on a break action single shot, I've got friends that love their Chiappa little badgers and they be grown ass men.
My thinking exactly. It depends how much you want to spend really and the kind of shooting you want to do or if he'd be into customizing his new rifle. Shooting off-hand at soda cans and eggs, I'm sure he would have fun with a Henry lever action but for focusing on marksmanship and benchrest shooting, a bolt action is the way to go and I'd lean towards a Savage Rascal or CZ457 Scout. Good luck!