If you can find a Remington 580 or 581 you will have a winner IMO... they are extremely light for a young person to carry but the accuracy of these rifles is off the charts in relation to their price point... I bought the one I have for my son when he was about 10 and he loved it then and still does... a bit of a long reach is something young guys tend to deal with pretty easily and they grow into them pretty quickly... in my experience.
Another one to look at would be a Winchester 69 Boy Scout or Youth model. They are kind of hard to find and demand a premium, but they have very nice walnut stocks, are built around a young person's reach, and are extremely accurate. Once your son gets too big for the length of pull, you will easily get your money back out of it by moving it along to another dad with a young son and getting a newer model fit a larger person...
