IMO - the episode the encapsulates 'Star Trek' for me is:
The Corbomite Manuever
(And I still think it's one of the best Star Trek episodes from any of the 6 series <-- I'm also counting TAS
The ship is exploring the edge of known space. All the characters have good bits in the episode, and there's some suspense and danger; and it's essentially a 'Fisrt Contact' situation as well.
And if you don't care for 'hokey special effects' show him the remastered version. Hell, even in syndication these days the channel show the series in my area is showing the remastered version of the episodes.