(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.
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.
Then you have Obrian's history with the Cardassians - quite significant for his new assignment and without this context the character feels like a fake tough guy. The acting and directing was brilliant, because we could feel the restrain, but without understanding this it comes off cocky. It's like watching Travolta's character dance poorly in Pulp Fiction - if you didn't know who Travolta was, the scene comes off poorly acted. Or Robin Williams playing a gay man playing straight. Some background of the character is important to actually enjoy the acting mastery that we are witnessing.
There are occasional TNG references but they are not important to the plot.
It’s hard for me to be entirely unbiased myself, as I watched the the original series (TOS) films without watching much of the OG series itself, and then watched TNG when it was airing, so I already had the context to watch DS9.
All of that is to say, I don’t think you necessarily need to watch TNG to appreciate DS9. The shows are mostly standalone and self contained. Also, I don’t think this is much of a spoiler, as the double episode premiere of DS9 pretty much includes all of what I’ve said above, in some form or fashion, with the exception of the introduction of some character crossovers of the TNG cast. I think it’s nice to know where those characters came from and what they went through prior to DS9, as the two shows were running concurrently, but neither show is written in such a way that you’ll feel lost if you don’t watch TNG first, though others may disagree.
TNG was far more thought provoking and one could ponder each episode - I'm still pondering some. Other than Sisko's decisions in the latter seasons, what years-to-ponder dilemmas were explored in DS9?
I actually felt that Sisko became a villian at some point, I wish that DS9 would have explored that.
Season 1: Ferengi
Season 4: Trill, Cardassians
Season 5: Bajorans
Also, Chief O'Brien and his wife Keiko who were recurring minor characters in TNG have more important roles in DS9.
Watch a handful of classic trek to get the idea. Balance of Terror, city on the Edge of Forever, maybe Mirror Mirror or Trouble with Tribbles. They will seem very cliched.
Start TNG in the third season and just focus on the best episodes, the ones that are 8s or 9s on IMDB. Be sure to see The Best of Both Worlds I and I, the original season finale climax.
Skip a lot of the first season of DS9. Low IMDb will tell you which ones. But watch almost all of the later seasons.
Then play Star Trek Attack Wing!
But all the star trek series are self contained enough that you don't really need to have seen the previous ones.
TOS and TNG explain the Federation utopian universe, the ongoing conflicts and races, the moral dilemmas of the captains... I feel that starting with DS9 might get you miss the point a bit.
I would say to at least try to watch a curated selection of TNG episodes.
Babylon 5 explores some aspects deeply which were just glanced over in DS9 and that makes it an amazing show as well.