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
Another bonus of showing them "Corbomite" first is that they won't be wondering what the hell the deal is with that freaky face thing at the end of the closing credits when watching other episodes.