Looks like .223 is a legal caliber in Oregon for deer?
Hunting Big Game: Weapons Restrictions - Oregon Department of Fish and Wildlife
Based on your question a .223 cal would be a good caliber to learn the basics and the ammo is not as pricey as 6mm. And although I have shot deer in States that allowed .223 as the minimal caliber it is a debate that this forum probably has 500 posts on.
Some would recommend he practice with the .223 but hunt with the .243
If you got duplicate rifles, triggers, etcetera it might be better. But if he simply shot both rifles enough at the range and field it would work too.
Since the NEF single shot was mentioned and I own one in 30-06 and 12 gauge I would second the vote for a NEF in .223 cal and get the second barrel (.243) for under $90.00 and you have killed two birds with one stone. The barrels change out in seconds. I carry my NEFs on my motorcycle all the time broken down. Not as obvious plus broken down less likely to snag a tree branch negotiating a trail.
The NEF rifle comes in a "youth line." Such smart people to hook us young and guarantee a buyer for years to come.
H & R Firearms: Firearms: Rifles