The thing I continually see in discussions about kids or women's guns is that gun weight is left out, or -- worse yet -- the gun is touted because it is light in weight. Should be just the opposite! Why? Principle of physics that every action has an equal an opposite reaction. So when the powder force pushes the bullet forward it also pushes the gun backward with the same amount of force. The greater the gun's weight, the more this mass can resist the gun's tendency to push backward with felt recoil.
I've shot some truly heavy-recoiling firearms, and among the worst was a single-shot "youth model" 20 ga. shotgun using a relatively heavy turkey load. These guns are continually given or auctioned away at fundraisers like NRA or National Wild Turkey Federation (NWTF)! Talk about a way to induce instant flinch and dislike of shooting in a light-weight youth or woman!
So in addition to using the lightest powder charge and bullet or ball, add weigh to the "youth gun". Some lead weights taped to the foreend, and perhaps lead added to good-sized holes drilled in the buttstock under the recoil pad.
And get a strap-on recoil pad and modify it to fit the youth or woman. Use a slip-on pad on the gun too (if the gun has no integral recoil pad), if that does not make the "length of pull" too long for the youth or woman shooter.
And lastly, very importantly, hearing protection that is truly good, which immediately throws out those simple foam earplugs I so often see. Young people have their hearing fully intact, and the noise of guns going off, above that of a .22, will also cause a flinch to develop. The trick is to use some cleverness to get the light weight person be able to get down on the cheekpiece area of the gunstock, without the earmuffs interfering with this critical positioning need. If their cheek is not firmly welded to the stock as the shot goes off, the buttstock comes up and whacks their cheek, considerably increasing "felt recoil". To young people especially, the sound of the gun going off is a part of "felt recoil" to them, and can cause flinching just the same as physical recoil. A scope, being set higher than open sights, makes this issue less important. Also, use the soft earplugs too, under the earmuffs.
I agree with using a round ball to start off with, but recommend at least 50 cal. for deer. That, and even 50-60 gr. volume of Blackhorn 209, should do you well for close-range deer.
Aloha, Ka'imiloa