TOS, although I’d start with season 1.

My friend best described it as “The US Navy, in space.” It’s definitely progressive, although you have to consider it was made in the 60s, and while there are women officers, it’s still a male-centric show, with women swooning over Kirk in a sort of James Bond way. Still, there’s a black, female officer on the bridge, and her job is arguable more commanding than, say, whichever ensign is manning the weapons that day, so… they were pushing the boundaries of acceptability for 1966 broadcast television. Basically, mankind is making progress, but the show still has to appeal to American public.

TNG has less of the swooning, and more equality for women. It ran for longer, and there’s a fair amount of dark and ugly later in the series; IMHO, the later seasons lose much of the optimism that we’re far from perfect, but generally getting better as a species and society. There are plenty of bigots in high command - which is what bothers me the most. Star Fleet is supposed to be the best of the best of us, and yet there regularly are some just awful people in high positions in Star Fleet, and it just frustrates me. It’s such a step backwards. But, as I’ve said elsewhere, I think ST generally reflects the level of optimism of the target audience, and by the mid-90s we had G. H. W. Bush in office, and we seemed to be involved in constant conflicts - Libya, Grenada, Panama, and the highly controversial Gulf War). While we had the space shuttle flying, after the first initial rush of getting to the moon, the space program seemed to have stalled; we didn’t seem to be making any progress to getting people into space. Shit, we hadn’t even set foot on the moon again since TOS (the last human to set foot on the moon did so 3 years after TOS was canceled). Still, especially in the first seasons, TNG is still probably still the most optimistic of the series.

DS9 was a fantastic series, but absolutely was not optimistic. It’s full of moral quandaries, questionable ethical decisions, terrorism, totalitarianism, genocide, ; of all the series, I think it encompasses all of the worst of mankind, even if it’s other races doing those things. Again, Star Fleet command is not represented as “the best of the best of us” which annoys me.

Voyager… I didn’t watch more than a few episodes. I really disliked the comic relief format and, TBH, most of the characters. I thought the writing was awful, in general; it started rough, but unlike TNG, it never found its groove. IMO.

And after that, I mostly ignored the seasons. In this time, there were a couple of real stinkers in the theater, too, and with the reboot… it wasn’t Trek, just a leech trying to milk as much money from the fandom as possible.

I picked it back up with Lower Decks, which I consider the first true Trek in the original Roddenberry spirit, despite being an animated almost-parody. It’s optimistic, Star Fleet is once again competent and staffed with reasonable, well-intentioned people. I’m not a woman, so I can’t say if it achieves full equality, but it feels like it to me.

Because of LD, I tried Strange New Worlds, and found it… not awful. I have a pet peeve about the obsession about sexualizing Spock, which started with the reboot, and it’s a major running plot device through SNW. Plus they’ve retconned the Born which is exceedingly frustrating. And in the first season they’ve already had two episodes with alt-reality; one fantasy, and one that’s basically a musical. Usually writers don’t resort to these until the show has already jumped the shark. I’ll admit that I fast-forwarded through most of the musical one. I’ll probably start watching season 2, but if there writers keep up with these filler plot devices, I’ll probably drop it. There are some really good episodes in the first season, though.

So, to echo parent: start with TOS, and then TNG. After that, you’re on your own.

Oh, PS Lower Decks is best watched after all of the others you’re going to watch, because a full 40% of the fun is the show poking fun at tropes from the other series. Many of the jokes will fall flat or just go over your head if you haven’t watched at least TOS and TNG.