It was the first Trek in years after TOS, and it had to basically re-introduce everything that later series build upon.
My dirty secret is that I've never seen TOS more than a few episodes, clips, or summaries of the higher-profile episodes. 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).
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.
I think Encounter at Farpoint is important for that hopeful view of the future that OP is looking for. It establishes what the Federation is as a power in the Alpha Quadrant, and also gives a nice basic moral hurdle for them to overcome. Plus, seeing Q's first appearance is kinda necessary imo
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.
It really honestly depends on what you want in a show. While TNG is fantastic, I'd actually recommend Strange New Worlds. It has a little of something everyone could want in a show in general while setting you up for all of the rest since it is a prequel to all of the other shows.
I agree with the others saying start with TNG season 1. Just know, some of the episodes are rough. They took a little while to find their feet. Check episode ratings on review sites, if you want to avoid the bad ones.
I've recently started getting a friend into Trek myself. They're more into DS9, because they've been seeing memes about the Bell Riots, so we've been taking it slow on the other series. We decided to do a Best Of for TNG to begin with. So far, we watched episodes 1 and 2, Encounter at Farpoint, as well as episode 12, Datalore. Then we skipped straight to season 2, and watched episodes 3, 8, 9, 16, and 21. We also watched episode 16, Samaritan Snare, but only because it's relevant to Star Trek: Lower Decks lol
I think Strange New Worlds could be a good start for someone entirely new to the franchise. Not too dark, a lot of vibes from the The Original Series and solid cast / writing.
Joking answer: Star Trek: The Next Generation season 1, but skip all episodes except "Code of Honor", which is the "best" in the franchise.
Serious Answer: DS9 season 1. Although it's less hopeful than the typical Trek in many senses, I think it still has that Trekian sense of ethics about it. Also, the characters are great, and the first season is much more watchable than TNG season 1.
I think it boils down to what kind of TV you want to watch in general, because almost all Star Trek is good Star Trek, but the shows are very much products of their time
So, do you want 60s adventure of the week where you really get into the origins of the franchise? -> Original Series seasons 1-2
80s/90s vision of a future where we have really learnt to better ourselves? -> The Next Generation Season 3 onwards (and any highly rated season 1 or 2 episodes)
A new take on Star Trek that keeps the hope and adventure, with modern special effects and episodes still in production / coming out? -> Strange New Worlds starting at the very beginning
The other shows are good too, but for someone specifically looking for a hopeful iteration of Star Trek, I'd recommend the above three
If you like b5, then DS9. Long drawn out story, more character evolution, more shades of grey.
If you like the orville, then tng, be prepared for early installment weirdness, it literally coined the phrase "grew the beard" because its levelling up coincided with Riker growing one. Lower decks also works
If you're experienced with 60's stuff like Man from U.N.C.L.E, tos will do.
If you're a 90's kid, ENT
If you're a 00's kid, SNW. Lower decks also works
Voyager is for more experienced trekkers, but they do batshit like no other
If you're looking for the hopeful view of humanity's future, I'd start with Season 3 of The Next Generation. It has that in spades, while also skipping over the first two seasons where it is really trying to find its footing. If you really like it and want to see how it all started, go back and watch the first two seasons.
If you like TNG and want a more character-driven experience that doesn't focus nearly as much on exploration, Deep Space Nine is fantastic. Just like TNG, the first two seasons are kind of rough as they try to figure things out. They're also a fair bit slower (some call them dull) than the later seasons, but if you like character and world building, they're pretty decent. It really gains steam with season 3.
If you want to continue the theme of exploration, Star Trek Voyager is good. I don't enjoy it as much as TNG and DS9, but Voyager has the advantage of the show runners and writers having fully figured out what life is like in that time period without the stumbles of the first two series. I'd say it remains fairly consistent throughout, but I personally don't find that its highs are as high as TNG and DS9.
Your degree of prior knowledge isn’t much of an issue. Every show explores its own little corner of the universe, and they all stand well enough on their own.
I’ll make an exception for Lower Decks - it’s full of referential humour that you’ll appreciate more if you’ve at least seen TNG first.
I’d say start from the beginning, unless you’re particularly uncomfortable with TV from the sixties. Most Star Trek takes a season or three to really find their groove, but TOS fires on all cylinders right out of the gate.
If you crave something more modern, Strange New Worlds is an excellent place to start, with the advantage that you can enjoy new episodes as season 3 comes out later this year.
TNG is a popular recommendation, but it’s a little dated itself, and the first season is strikingly rough around the edges.
If you're over 40 years old, the original from 1966. Otherwise it depends on your sensibilities. If classic men with rockets boldly exploring stuff feeling is too much, TNG is the popular choice these days I think. Personally my second favourite (after TOS) is Voyager.
Which season? You mean which Star Trek, right? Do you want: 60s Technicolor and skirts; Animated not because it's for kids, but because special effects are expensive and difficult; Androids and friendly Klingons; Frontier space station; One ship alone against an entire quadrant of the galaxy; Time travel and a theme song with words; Tripping through space with the help of mushrooms; Animated, this time for kids; Star Trek, now with more heart; Star Trek: beyond retirement; Star Trek: humor will set us free?
Opinion: if you go in chronological order, the age and quality will progress nicely, rather than jumping all around if you start with one then go back and do that sort of thing.
All these posts, and not ONE person mentioned The Animated Series. No, not that one, the older one.
It's unorthodox, sure, but it's also a pretty low stakes and less uh, of-its-time, way to enjoy some TOS before going into TOS, which is 100% where you should start.
TNG is the most uplifting, imho, but as the others have said, the first seasons are hit and miss.
If you can make through the fourth episode, which is widely considered one of, if not the worst, whitout wanting to quit right away, you'll bei good, it only get's better.
If not, skip ahead to season 3.
Also, everything looks more modern from seasons 3 onward, if the 80s look bothers you.