For a starter rifle, you could do worse than a Remington Model 7 in either .243, .260 Rem or 7mm08. The Model 7 even came in a youth model, if I recall correctly. When he outgrows the youth stock, you can find all kinds of aftermarket stocks (mostly glass, not wood, but wood is available).
If you're going to go something other than bolt action, I'd stay away from the single shots. I think you'll find them more of a specialty item than a youth rifle. My recommendation would be either the Savage Model 99 in .300 Savage, .243, .308 or .250 Savage or the Winchester Model 88 in either .243 or .308.
FWIW, I started all three of my boys on a used Savage Model 340 bolt action .30-30. They weren't pretty, but they were functional, had a detachable magazine and were light enough that the kids could carry them. The .30-30 is an effective deer killer out to at least 150 yards and most kids shouldn't be shooting even that far except off a bench. The rifles use a side mount for a scope, but they are easy to find. The older ones weren't drilled and tapped so look on the left side of the receiver or find one already having a scope mounted.
