I think neither Amok Time, Naked Time nor Mirror Mirror would be good episodes to start out with unfortunately. As second or third episodes they would of course like any episode be selectable, depending on how you've organized his introduction.
The only reason those episodes seem like they might be ok is that there have been a ton of pop culture references made from them, and that recognition might help hook him in. That said, I do see your point.
Well, it looks like a ton of recommendations for Balance of Terror, which isn't personally a favorite of mine, but seems logical enough. I fell completely in love with TOS after The Enemy Within, but I think that's just me. Balance of Terror probably would appeal to him, so I'll probably go with that for the first one.