I'd personally recommend:

    * The Next Generation (starting point, but be prepared to sit through the slower first seasons).
    * DS9
    * Voyager (however optionally skip anything from the Kess seasons that you feel like)

I only liked about 1/3rd of Star Trek Enterprise episodes, the entire series is kind of filler. Has that same wasted potential feeling that I got from Stargate Universe; it COULD have been more interesting if the pacing had been better and if they had focused on fitting the stories in to an overall plotline (much more like Babylon 5; which, BTW, you should TOTALLY watch if you haven't).

Star Trek Discovery was good, but is more an edgier more action packed thriller kind of series than the earlier series. I do like where they're going with rebooting the overall universe though and I feel that this brings the modern FX capacity in to the series in a way that makes sense for today.

For something you can show to your parents or if you generally don't get Star Trek, the Orville is a GREAT comedy focused take on the ideas that Star Trek (everything) classically presented, but covering modern social issues.