Ask the general public what is their favorite Trek series and they will say TNG or TOS based mostly on nostalgia. Ask a Trek fan who have seen all the series and they will say DS9 and rightly so.
The stories are much deeper then any other trek series and mean something on the whole of the series. Characters are deeper, but more importantly actually grow and change. The side-cast has some of the best characters in all of Trek and their stories are not one off, one time episodes. There are many more reasons, but the most important one is that DS9 is the darkest Trek out there. And no, not edgy like Discovery, but actually dark. DS9 explores controversial topics that Trek has generally avoided like religion and genocide. Here, things are not black and white. Everyone, even the federation is a shade of grey.
Episodes to note:
The Visitor (S4E3)
Far Beyond the Stars (S6E13)
Trials and Tribble-ations (S5E6)
Duet (S1E19)
In the Pale Moonlight (S6E19) - The best episode in all of Trek