I wanna say “the corbomite maneuver” from TOS. I think it’s one of the best episodes of all, but most people don’t so i think it’s okay from the its all downhill perspective. It has everything: Kirk mentoring, an extremely powerful alien of the week, solving problems without fighting, but still tense situations. Such a great and representative episode.

From TNG maybe First Contact. Good intro episode as you get intro to the federation through the eyes of an alien of the week. The alien-chasing woman may be not a good thing to show depending on the person you’re showing it to, though.

For DS9, in the hands of the prophets. Doesn’t require much backstory unlike a lot of DS9, great ep, classic ethical debate/social commentary, and the majesty that is Vedek Winn.

For Voyager maybe distant origin. Great ep, doesn’t need much backstory, also great commentary on society