Good advise so far. I see this as a good excuse to get the wife to approve buying a gun since its for the kid. Whats the difference between the 7-08 and the 308? Really leaning towards the 308 since I have quite a bit of ammo for one already.
The stock length a person requires is a bit like archery draw length and height isn't everything. One must also consider how wide across the chest they are. Tall and thin (say 5'10" or less) of either gender can likely benefit from at least 1" shorter length stock. My wife is 5'9" but a standard length rifle or shotgun would be too long for her.
A rifle or shotgun that's too long results in WAY more felt recoil because the rifle is mostly out of the shooter's control from the get go. A stock that's too long contributes to shitty form and shittier shooting experience. Case in point:
If you hand your kid a long-gun and they resemble the above picture, stop, do whatever needs doing to adjust the stock length to the proper dimensions.
Leaning back: There's only the shoulder to absorb the recoil, the rifle in the above pic has 8-10" of "head start" on the recoil and the shooter has no place to go, the pivot point for recoil is above the belly button and essentially the shoulder has to take all of the punishment. Properly fitted, the pivot point for recoil should be your ankles so your whole body can absorb the recoil, not just your torso above the BB.
Cheekweld: Often when stocks are too long like the above, you see the shooter just rolling their head over towards their shoulder to establish cheek weld and sight/scope alignment of their eyes and the device, depending on the rifle, you end up behind the Monte Carlo cheekpiece. When that happens your view through the scope is shitty and the sharp rear edge of the cheekpiece smashes you in the face. A properly fitted stock allows the shooter to move their head forward and down and perch their cheek upon the top of the stock allowing for a comfortable placement of the head that also allows more control of the firearm under recoil.
Last thing to remember regarding stock length is that we often have kids try guns in their street clothes and then add several layers when they're actually hunting.
I like to think I'm at least moderately experienced with both a rifle and a shotgun under field conditions and I can say I have virtually no trouble shooting a rifle or shotgun that's too short for me. I can back my head off of a stock a little to find the proper spot for a full view of the scope and I find a short-stocked shotgun to be lightning fast to shoulder. I find that trying to shoot either one that's too long for me to be damned challenging.
The above picture tells the story far better than if I'd write another 10,000 words. Don't make your beginning shooter of any age or gender shoot from a position that mimics the above.
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Regarding the actual question from the OP. If you have access to a bunch of 308 ammo, that makes the decision easier. More ammo = more shooting = more better.