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.