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@The Nemesis, here's my "You need to have these people watch these episodes if they've not watched Trek. I'll start with Enterprise.
1: Broken Bow - where we first meet our plucky crew of the NX-01 and learn about everything the series will be about.
2: The Andorian Incident + Shadows of P'Jem- where we first meet the Andorians, and we truly see this is the 'wilderness' years of Starfleet, nothing is happy plucky go lucky, Federation. Vulcans are shady as hell, and the Andorians are cool. (also. Jeffrey Combs. the end). also these two episodes have consequences that you feel through the entire series
3: Fusion + Stigma + This will actually show you everything we knew about Vulcans before was off. Mind Melds seen as Taboo? this also triggers T'Pol's entire storyline through the rest of the series, these two events. (as well as other episodes as well)
4: Dear Doctor: Basically the premise/birth of the Prime Directive. (I'm pretty sure it's this episode). The PD is something most people love to debate, and to see it in it's first forms I think is necessary.
5: The Expanse: Signals the end of "Enterprise trying to be 'Star Trek' - and deciding to do its own thing and being better for it. (even though it creates an event that no one knew about in the future - the Swatch cut from Florida to Venezuela, triggering events between Trip + T'Pol (yet not explaining why Trip: was born in Florida, raised in Florida, still lived in Florida had a drawl stronger stronger than a glass of sweet tea). and basically creating Braga's "Year of Hell" (that Voyager should have had) - but in Enterprise.
6: Impulse, Azati Prime and Damage. I'm cheating but i feel these three stories are linked. This is where we see the climax of what Fusion/Stigma impacted on T'pol, how far Archer will go to do things (more so than any other Captain, maybe excluding Sisko). and - actiony bits!!
7: Borderland, ColdStation 12 and the Auguments; Season 4 is "arch" season, so I think truly, it's a given that some of these arcs would be suggested. This one has ties to TOS, + DS9 (genetics) and of course TNG (with the cybernetic shoutout at the end). also it ties into
8: Affliction + Divergence (Though - if you thought this was a cop out to explain the Klingon Ridges - you could by pass this)
9: The Forge, Awakening + Kir'Shara: basically explaining how Vulcans became Vulcans (before) and how they'll become Vulcans that we know and love (later), including mindmelds. EVERYTHING (from the first few suggested episodes, come to ahead here as well). also. we get our first hint of reunification (why it's always Romulans who want to Conquer Vulcan vs. them coming together in peace is beyond me this is never addressed
10: Demons + Terra Prime - basically how the series should have ended and you saw the heading of Coalition of Planets
HM: Regeneration... basically anything in season 4 (like more Andorian/Tellerites stuff, and things that showed how in season 1 - how far apart everyone was, and how in season 4 - it makes total sense for them to even talk about being a federation (at somepoint). Oh, you could do the Organians episode as well. actually i would for sure.
Would totally avoid: anything with the temporal time war. That crap made zero sense to me (and you can sort of hand-wave it in Broken Bow). I still don't get how the Suliban people are even involved in it. I know i cheated with the arcs - but i think with Enterprise (and DS9) as they were more serialized than the other series, you kind of need to do 'arcs' with those shows. you could though HM most of the arcs and pick the 'best story without missing too much I think.
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