i'm in a similar situation with 10yr old, he's a bit immature but showing some interest, he's not bad on the air rifle.
for me i just don't think you can beat the .308, reduced loads with 2206h (60% rule) and a soft 150-168gr bullet, increase velocity as they grow.
a super lite might be just that bit too light with recoil? the new howa is only 2kg, but you might still want to shorten the stock a touch.
i thinking standard sporter weight howa, 20" barrel would be nice rather than the standard 22". hogue do a compact stock if you can find one with a 12.5" length of pull.
other options for me are tikka t3x lite with a compact stock (most expensive option). or ruger american compact, 18" barrel, 12.5" LOP stock.