It’s difficult for me to answer in an unbiased way because I grew up watching the shows during their original run and I generally watch one or two of the series runs each year. I watched TOS earlier this year and am presently part way through VOY. Did TNG last Christmas, might do DS9 this Christmas. I’ve got history with these here shows.
It might be better to watch TNG first to see what Roddenberry was going for and see how he set the Star Trek “rules” so to speak before you see how they were broken in DS9 as that might have more impact. TNG might seem a little quaint after watching DS9.
As for Voyager… VOY is effectively an alt-TNG and not really distinguishable but also not offensive if you throw out the space salamanders and similarly horrid episodes. VOY started with the premise of being a series about a ship on its own trying to get home and having to deal with limited resources and always scrambling for fuel and water or whatever, but that sense of desperation lasted about 3 episodes before it reverted to TNG Part 2. It could have really been something but they didn’t have the guts to push any boundaries. Battlestar Galactica 2004 feels like that concept done correctly before it kind of went off the rails when they forgot what show they started with, but I digress.
I think you’d appreciate DS9 more by letting TNG set the stage. DS9 also primarily occurs chronologically after TNG for the most part, with some overlap in the early seasons, although that barely makes a difference in the narrative. Watch TNG for the vision, watch DS9 for the vision rearranged, and bear in mind that these are 30 year old shows before CGI was common place. There will be some racism and sexism in the early TNG episodes and the VFX will be spotty, but these are classics for a reason.
