I posted earlier:
Take the ones you are comfortable letting him pursue elk with, lay them out -- address the " fit" issue with each one, train him on the fundamentals doing a bunch of dry fire, go light on the bullet weight, let him shoot them and then let him choose.
Just a follow up to that one:
HOWEVER, if he lumps all the elk-capable rifles that you have to offer in with the 3" 20 gauge, that is too much recoil, then I' d say the most elk hunting the lad ought to do this year is hike along, check out the action, whet his appetite and grow up/toughen up a little more -- regardless of his physical size now. Once he sees what is really involved he may change a lot in a year and have more fun this year.
[No comment on 30-30' s for elk, especially when in the hands of a novice.]
It is a good thing to take a young one hunting,
EKM