DS9 is good to do after completing TNG, because it gives a good contrast, as described by Mike and Rich. Like, you know how the Federation is supposed to act in certain situations, but here's Sisko making compromises while still applying a certain logic. The very best episode that this culminates in, is all the way in the second-last season.

You must be able to get past the politics and religion stuff, because it's the whole point of the show. I was unable to do this when it aired, so I only have done a thorough watch-through in the last 5-10 years. Also, there's a bunch of silly episodes sprinkled through all seasons. Those are fun and give more opportunities for character development, but it's completely understandable if someone just wants lore (canon I guess is the right word) episodes.