How do they hold up?
I am very familiar with these shows from watching them a lot as a kid but I also did the weird thing of kind of outgrowing them. So twenty/thirty years later, I approached them without any great reverence. I also was doing jigsaw puzzles a lot while watching them.
First I did TNG. I never thought of the first season as the godless abomination everyone else does and I still don't. But I definitely saw the problems a bit more. For one thing, oh yeah, Wesley is that bad. There was a string of around a half dozen episodes where the wunderkind was the key to saving the day. I also noticed the technobabble that Voyager gets it in the neck for really emerging in the last couple of seasons. But I also felt there are so many unsung gems. 'The Survivors', 'Hollow Pursuits', 'Remember Me', 'Half a Life', 'Cause and Effect', 'The Next Phase'. I even liked the goofy season 7 stuff (except the cringy 'Sub Rosa'). I would it holds up pretty well, though Geordi turns out to be a bit of a creeper in 'Galaxy's Child'.
Next on to TOS. 'The Cage' still holds up but so does a lot of stuff. There is a fair bit of values dissonance with gender politics of course (a woman is of course going to leave the service after she marries, duh). It was interesting to note how much Kirk's reputation as a poon hound is not actually deserved. He's had a few girlfriends, but they weren't the conquests of a dude bro. And his seduction of the alien woman of the week was usually just Kirk using sexuality as a weapon to overcome a captor, not something motivated by his own lust. Expecting some of the values dissonance and camp, I would say this holds up very well.
Then I just finished DS9 and this was the one that held up the least. To be honest, world building in Star Trek has never been great. Everything, including iconic aspects like the Federation, Vulcans, Klingons, is poorly thought through. But DS9 was much more dependent on the depth of world building than the other shows so it really suffers more, even though it does try to build things up more. In a show that is telling stories about great power politics, having the captain make decisions that the president of the Federation or the Federation council should be making really shows the flaws in the Starfleet centric approach of the writers. It gets to the point where it inadvertently depicts the Federation as a military dictatorship. Why is the ceremony to admit Bajor into the Federation attended by Starfleet admirals and not the president? Why is Richard Bashir, a civilian, being sentenced for his non-Starfleet crime by an admiral? Why does Starfleet medical possess the only historic medical records of Odo? Episode after episode had these world building problems. Still, Marc Alaimo, Jeffrey Combs and Andrew Robinson are all fantastic in every scene they're in. When the show was good, it was great. I still put 'Duet' as the greatest thing the franchise has ever produced with 'In the Pale Moonlight' not far behind and the arc at the beginning of season 6, outside of the Alexander bit, was fantastic. But the less said about the pagh wraiths the better.