I bought the first three seasons of TNG recently and am working my way through those. I thought about buying DS9, but I decided to wait until I got to the point in the TNG timeline that DS9 came about. I thought watching them concurrently would be a good way to go about it, otherwise plotlines/spoilers would likely be a problem (I only caught the first 4 seasons of DS9 back in the day, and in watching just the first season of TNG, I've found I missed a fair amount of episodes from that series as well).

I have fond memories of DS9 and always considered it a strong series. I'm looking forward to checking it out.