I'd go with The Trouble With Tribbles.
I still think you need to have a baseline knowledge of the characters for that episode to have its full effect.
If the viewer does not know anything about Kirk, Spock, Scotty, McCoy, or Chekov to begin with, then the intentional caricatures of themselves that were presented too us loses their meaning.
I think it's the same with The Naked Time and Mirror, Mirror.
Now that he has seen Balance of Terror and liked it, maybe you should just let him watch the episodes in either production order or airdate order.