ORIGINAL: The Rifleman
I will agree with anyone that says that you shouldn't use anything smaller than a .243 Winchester and go one step further to say that a .243 shouldn't be used as a kids gun because you have to be selective in where you shoot to make a ethical shot on a large whitetail deer.
JMO, but, it seems to me that if you've got a kid shooting, he's going to be a lot more likely to flinch and gut shoot a deer with a .30-06 than he will with a .243. The last part of your sentence implies that you don't have to be selective where you shoot to make an ethical shot if you are using a larger caliber. That's just not the case. Shot placement is important regardless of caliber, and I'd rather have my son focusing on where he's placing the bullet than worrying about the recoil of a larger caliber, and yanking the trigger with his eyes closed... If you put a .243 through the deer's lungs because you've been practicing and can hit where you aim, you're going to have a lot deader deer than if you gut shoot him with a .300 RUM because you're afraid of the recoil...
The .243 seems to work fine for him.