Both my boys killed there first few deer with a 357 Mag Handi-Rifle. I loaded some 158gr JHPs and was very impressed with the performance on deer out to 60ish yds. That said, if I had the option of using a 223 I would likely have went that direction. I have full faith in either, but feel that the 223 offers greater range with little/no penalty.
Unless the kiddo is already versed in using a scope, I'd strongly recommend a red dot. So very intuitive for the kids. No eye relief/paralax issues. My youngest head shot a groundhog a 90yds with the thing!
