There is some science behind the .243 being close to underpowered. I know it is plenty sufficient, but what happens in the event of a quartering to shot. If it hits shoulder an 85gr bullet might not drop a big deer after it hits shoulder. If you shoot a 115gr bullet it might help your chances, but now with a simple broad side shot without hitting ribs on either side, you would likely get over penetration and not do enough damage to drop the deer quickly. Does a 100gr solve all the problems, maybe maybe not.
Chuck hawks has a great article about this entitled "The Sectional Density of Rifle Bullets"
He recommends for deer sized game 95gr bullets with the .243 caliber. (sectional density .23)
Momentum is needed to break bone and the heavier the bullet, the more momentum. As you increase the weight of the bullet recoil will also increase.
So in order for recoil to stay the same velocity will have to decrease as weight increases.
As velocity decreases, ballistics drop. But since where this hunter is going to be hunting will not require shots over 100 yards, ballistics is the least concern. So it appears that slow heavy large bore bullets would be the best choice.
[As an aside, larger bore bullets tend to accelerate bullets more efficiently, because essentially there is more surface area on the back of the bullet to push on. It is much more complicated than that. But if you put 10gr of powder behind a 100gr .243 bullet and shoot out of a 20" barrel and then do the same with 10grs of powder behind a 100gr .308 bullet the .308 will be going faster. Since powder charge is a component of recoil this actually makes larger bores recoil less, which is counter intuitive... correct me if I'm wrong here.]
Common slow heavy large bore bullet... Most handgun bullets. Say 44 Mag, only problem I see with this round is when is comes time to "take a trip out west" or "go hunting for Moose or Black bear" you can't really step up without going to a different gun.
Thats why I thought the 45LC, 454 Casull, 460S&W was a good combination.
Bottom line I'd rather see the kid learn the trajectory path of a bullet rather than how to track a wounded deer.
I don't mean to act as though I am answering my own question, but I feel if I can convince you guys of this stuff then I may have a good point, and if I can't than maybe its all just mathematical BS.
As for most of the calibers people are recommending they all seem good. They all also seem to agree with another chuck hawks article "Sensible Rifle Cartridges (Includes the 6mm Rem., .257 Roberts, 6.5x55 Swede, 7x57 Mauser, .300 Savage, .338 Federal and .358 Winchester)"