Sector 7 wrote:
Your list would definitely overwhelm your friend. Here are a couple of essentials that I like:
Where No Man Has Gone Before
City on the Edge of Forever
The Inner Light
Trials and Tribble-ations
The Caretaker, Parts 1 & 2
This short list can be a primer for those wanting to know more about Star Trek. IMO, it also comprises some of the best of Trek series.
I'm not sure that Trials and Tribble-ations makes sense without first having seen The Trouble With Tribbles, though.
As for the other series, I would substitute "Year Of Hell" for "Caretaker", and "Shuttlepod One" or "Observer Effect" for "Carbon Creek". Or perhaps one of the S4 arcs - "Babel One"/"United"/"The Aenar" might be a good choice.
For Q episodes, "Encounter At Farpoint" is a must because it introduces Q, "All Good Things..." because it brings the story full circle, and I'd throw in "Death Wish" from VOY because it deals with the whole omnipotence thing and its pitfalls.
I can't disagree with any of Sector 7
's other choices, though I'd also add "Cause And Effect".