It's always been my opinion that you're more likely to waste your money buying cheap toys that inhibit their chance of success. Whether it's a BB gun, Fishing reel or a bow. Buy something that'll actually function properly and teach them how to use it and they'll enjoy it. Set them up to fail and they'll get frustrated and go play Xbox.
I bought my son a PSE Spider compound, sights and release at six. He started out shooting at balloons in my shop at about 5 yds, now he's 17 and prefers bow hunting over rifle hunting.
Also enjoy it while you can they grow up real fast.