I am currently working on a Savage 111 in 243. Making it into a gun for my grand daughter. The oldest is 5 and pretty skittish, so not shooting rifles yet, but does shoot her pink BB gun. So working our way up the ladder and have plenty of time before she will shoot it.
While I do not think a 243 is an optimal deer caliber, it is certainly a tried and true performer with proper shot placement and bullet selection. The recoil is as light as a true deer caliber can be, so a solid choice from that perspective.
The 111 has wooden stock and standard weight barrel, as I remember it is 22". My plan is to refinish the stock, maybe FDE color or possibly something pink, maybe dipped in the Muddy Girl pattern. Barrel and action are blue and in good shape, so like remain as such.
I agree with DCW above, a normal "hunting" weight rifle in 308 has a lot of recoil, IME.
I have a Rem 700 varmint in 223 that will likely be the first high power "bench/target" rifle for my grand daughter. I say bench as it is too heavy for most youth to handle in a hunting situation. It has a 26" heavy contour fluted barrel, so recoil is almost zero, little more than a 22 mag.
No matter which rifle any youth shoots, hearing protection is an absolute must, so noise is not a huge factor. But a muzzle brake takes the noise to a different level, the concussion of a brake can be as scary as the noise.