Interesting project: I am getting ready to introduce my nephew to Star Trek: Deep Space 9 (DS9), so I have been reviewing the series to find those episodes that will best move him along the chain of the story.
Here is what I have so far for Season One.
Episode 1 "Emissary". I shared this with him a few weeks ago and he loved it. This is one of my favorite episodes of any science fiction television program. Based on the experience of viewing this show, he signed on.
Episode 2 "Past Prologue". This second episode introduces us to Garrick, his friendship with the Doctor is set up, and the friendship of Jake and Nog is set up. Keiko and Miles are having trouble on the station and Keiko starts the school. In addition, it brings up the question of Kira's loyalty and answers it. Although the show doesn't bring us into the major plot line that the show will follow for all seven seasons, I think it is very important as a connecting link to the greater story.
Episode 9 "Move Along Home". Although this is technically a stand-alone episode, it does advance the greater plot by introducing us to the first Gamma Quadrant aliens. It is a terrific Quark episode and generally just a lot of fun.
Episode 10 "The Nagus". I am a huge fan of the Ferengi story arc on DS9. The first time I saw this episode, I almost pissed myself laughing. Wallace Shawn's Zek is hysterical. It introduces the Ferengi practice of selling the vacuum desiccated remains of the dead, brings up more Rules of Acquisition and shows us much about how the Ferengi live. I'll bet my nephew loves it.
Episdoe 19 "In the Hands of the Prophets". I think this one would have to be included anyway, as it develops the story of Minister Jaro and Vedek Winn and of the whole Bajoran political scene. It develops further the relationship of Kira and Vedek Bareil and introduces us to the hostility between Kira and Winn, something that will last all seven seasons.
There it is. Should I have included the episode where Kai Opaka is lost to the Gamma Quadrant planet? The episode isn't that great and I can explain it in a few sentences.