Star Trek Canon Recs ST:TOS Must See 1.14 Balance of Terror - introduces the Romulans 1.22 Space Seed - set the stage for STII 1.26 Errand of Mercy - cements Fed-Klingon relationships in the 23rd century 1.28 The City on the Edge of Forever - one of the highest fan-rated eps 2.1 Amok Time - introduces Vulcan; Spock gets dumped at the altar 2.4 Mirror, Mirror - introduces the Mirror Universe, revisited in DS9/VOY/ENT 2.10 Journey to Babel - introduces Spock's family (Sarek had his own following) 2.15 The Trouble With Tribbles - fluffy (literally!) & hilarious ep; revisited in DS9 3.10 Plato's Stepchildren - blah ep famous for historic first televised interracial kiss
ST:TOS Other Suggested Picks 1.15 Shore Leave - plenty of slashy subtext 1.16 Galileo Seven - great character growth ep for Spock 1.25 Devil in the Dark - introduces the popular Horta species 2.17 A Piece of the Action - fluff and crack STII - fan favorite movie STIV - my favorite movie STVI - also fan favorite movie
ST:TNG Favorite Picard-centric 1.9 The Battle (backstory ep, featuring Stargazer & Ferengi) 3.18 Allegiance (kidnapped as labrat) 3.19 Captain's Holiday 4.20 Qpid (Q does Robin Hood) 5.2 Darmok (ignore the fridge logic of how language/the universal translator works) 5.7-8 Unification 1&2 (+Data +Spock) 5.25 The Inner Light (highest fan-rated Picard ep) 6.10-11 Chains of Command 1&2 (tortured by Cardassians) 6.15 Tapestry (Q does It's a Wonderful Life) 7.25-26 All Good Things 1&2
ST:TNG Favorite Data-centric 1.13 Datalore (introducing the evil brother) 2.9 The Measure of a Man (rights of artificial life in court) 3.16 The Offspring (briefly, a daughter) 3.22 The Most Toys (kidnapped by a collector) 4.3 Brothers (revisiting Dad & the evil brother) 4.11 Data's Day (a day in the life...) 4.25 In Theory (attempting to date) 5.26-6.1 Time's Arrow 1&2 (time travel with Mark Twain) 6.9 The Quality of Life (championing other artificial life) 6.16 Birthright 1 (dreaming for the first time)
ST:TNG Other Suggested Picks 3.4 Who Watches the Watchers (Picard gets mistaken for God) 3.13 Deja Q (Q finds being de-powered not-fun) 3.15 Yesterday's Enterprise (where Sela in Unification came from) 3.23 Sarek 3.26-4.1 Best of Both Worlds 1&2 4.7 Reunion (quintessential TNG Klingon ep) 5.5 Disaster (Picard in a lift with 3 kids, singing) 6.7 Rascals (Picard & others get de-aged) 7.9 Force of Nature (in it just for the cat, plus some Data/Geordi banter) 7.15 Lower Decks (focusing on the lowbies of the Enterprise)
EDIT: Various images I came across on my way to choosing my icon.