When my son was a few years younger than yours I bought him Tikka T3 Lite in a .243. The good thing about a Tikka is that it is an adult rifle but it has a shorter pull than a Remington 700. Another good thing is that it comes with the trigger set at a good weight, around 3.5 pounds. Where as a Remington (and most other American guns) come with a 7.5 pound pull. The reason I keep comparing it a Remington is because that is what I shoot. I love my Remington 30.06 and it will shoot a sub 1" MOA at hundred yards (after I had the trigger adjusted). However, it is too big for most kids 12 and under.
I would suggest letting him shoulder and work the action of several guns. What feels good/comfortable to him? What can he shoulder and hold steady? If my son was 12 when I made the purchase I would buy the largest framed gun that he could shoulder and hold still free handed. Caliber wise I would probably buy 7mm.08. You want something that is comfortable enough to shoot a lot at the range and as much as love my 30.06 I think it would develop some bad habits in a 12 year old at the range . He will probably start flinching to brace for the recoil without even knowing he is doing it. Flinching and heavy trigger pulls = missed or worse wounded and unrecovered deer.
I would suggest letting him shoulder and work the action of several guns. What feels good/comfortable to him? What can he shoulder and hold steady? If my son was 12 when I made the purchase I would buy the largest framed gun that he could shoulder and hold still free handed. Caliber wise I would probably buy 7mm.08. You want something that is comfortable enough to shoot a lot at the range and as much as love my 30.06 I think it would develop some bad habits in a 12 year old at the range . He will probably start flinching to brace for the recoil without even knowing he is doing it. Flinching and heavy trigger pulls = missed or worse wounded and unrecovered deer.