First couple seasons of TNG were pretty rough. If someone told me the first episode of something I should love was "Encounter at Farpoint", I think I'd drop the show after the first episode.

I'm going to suggest something different: Enterprise Season 1 Episode 1.

A new watcher would be on nearly equal footing with the crew in discovering the galaxy beyond Earth. Many of the same frustrations about being held back or being naively altruistic would be genuine human responses new viewers could identify with.

Responding to your edit:

Didn’t get into Trek until long after TNG was off the air, and don’t know if I could sit through the dated production quality of TOS (nothing against it; it was a product of its time and budget).

Some years back the production company replaced all the exterior physical model shots with pretty tasteful CGI. They also cleaned up the image quality and sound of the live action. It was a gentle but successful attempt at addressing some of those production value concerns you have. However, it does nothing for the inherent misogyny in the stories or costume design. I don't have much of a problem with that because it was progressive for its time.

A great way to watch TOS is to read about the show and the real life historical context of when they were produced. The US was deep into the war in Vietnam at the time and the show was airing episodes questioning the idea of regional power struggles, asking questions about racism, sexism and religion when people were matching in the streets with MLK.

TOS can be a bit slow because the way they produced the show back then was like a stage play with a captive audience. So it just means you get quite a bit of time during the show to read up on things and trivia while watching they program.

We're taking our time watching TOS because there are only a limited number of episodes but for many episodes it's really interesting to learn more about the time period they were produced and aired.