alt Hacker NewsProbably you should really watch TNG first, lots of characters and lore that would be needed to fully appreciate a lot of things that would otherwise fall flat at best or be outright not understandable. I don't think they matter to understanding the main arc but then the main arc is only a small part of the show.
(Voyager is entirely optional but a much welcome addition that happens concurrently at later seasons; I would recommend it on its own anyway.)
For all these shows, let them grow on you, the first season of each can be a bit awkward but then things start to fall into place, both in terms of characters/lore/setting/story/world building as well as actors themselves getting the hang of characters.
And yes there are absolute duds of episodes, but don't let that make you miss the absolutely fantastic ones.
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Voyager spoils the TNG experience by rehashing so many stories - definitely watch TNG first.
Not knowing the established history of some characters can actually be nice I think. The difference between a blank slate with conveniently made up background and a background that has already been told, in quite some detail, that difference tends to be very noticeable. No matter how "complex" the background made up on the spot is.
When the background has been told elsewhere, it's a legitimate challenge to the unprepared viewer's mind. But when it's made up on the spot, it's an arbitrary riddle. I know some viewers love that kind of stuff (e.g. everybody who made it through Lost I guess?), but to me that just feels annoying. If you want me to apply myself to the riddle, make it part of the story (like in a whodunnit), or don't keep me guessing.
But when it's organically grown background complexity from another story, I'm perfectly fine with it. Patrick Stewart's Gurney Halleck: he just pops up later with atomics, the "how" is not part of the movie adaptation. And neither is speculating about it. It's just an obvious indication that yes, there's more happening in this universe than the part squeezed into anamorphic cinemascope.
That being said, yes, watching TNG after DS9 wouldn't work well at all. It's hard enough watching early episodes after late episodes, because even the "adventure of the week" episodes have been told very differently later, but the universe is too much the same to really disconnect.