I would not only start DS9 before watching all the TNG movies, I'd consider starting it before finishing TNG. After all, they overlap in time period both in-universe and in terms of production. Specifically, season 1 of DS9 happens roughly concurrently with season 6 of TNG.
It's not overly important to watch it that way, but at least it avoids continuity weirdness with O'Brien and Worf.
I'd recommend DS9 Redefined, basically a group ripped DVDs and used AI to make a definitive remaster. They have instructions to download it in their Discord: https://discord.gg/AdMrnJ63
I think you can just jump into DS9 at this point? Its for the most part self contained, with some imported characters from TNG, but nothing that would require knowledge of the movies? Its a great series, with a planned arc ala babylon 5 (some very close similarities with babylon 5... very very close)