TNG and DS9 are the only two series that I really know well enough to make these recommendations for.

I would highly recommend watching TNG before DS9, even if she likes DS9 better. TNG and DS9 work best as companion shows, with TNG building up a lot of DS9 plot-lines in its latter seasons. I would also highly recommend against starting with any episodes involving Q or the Borg, or any of the series “highlights”. Let those plots build, and you don’t want to spoil some of the best episodes in a sampler. My go-to TNG introduction picks are:

-Cause and Effect

-Darmok

-Measure of a Man

DS9 can be harder to pick introductory episodes for. Its more serialized nature means that a lot of later episodes have a lot of spoilers. I would highly recommend against picking any episodes that highly involve the Dominion or the Dominion War, let that plot build itself up. That does however, leave us with a lot fewer options. My DS9 introduction picks are:

-Duet

-Past Tense

-Bar Association

I won’t stand for this “Ode to Spot” slander. It’s Data’s underrated masterpiece!

Mike using his YouTube money to buy and preserve old TV and Movie props is the best arc. Maybe in his retirement he can curate his collection

Picard starts every day by broadcasting “Space… The final frontier” to the crew

Disappointed that Marina Sirtis wouldn’t interview, though I kind of get why. Her role as a woman on Trek is certainly one of the more… complicated ones.

I have not but I’ll have to check it out. William Shatner and Leonard Nimoy being time travellers from the future would certainly be a twist!

This is an idea I ran by a fellow Trekkie awhile ago. An “Ed Wood” like movie about the behind the scenes of TOS. Satirize it from a place of love, focus on the drama between the cast and the antagonism between the studio and Gene. Quality movie material!