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.

I recommend The Next Generation. I find the crew in that series to be more variable and interesting, and the production is obviously more modern. You might be interested in the crew member Data, who is an android, considering the tech nature of HN!

I too recommend TNG. If you get to the end of the series and you still want more, there's also Voyager, which is essentially the same as TNG and slightly more modern.

As a companion read to diving into (or back into) ST:TNG, I have to recommend what is still quite possibly the best pop-culture essay I've ever read: http://grantland.com/features/next-generation-turns-25/

I'm more a fan of the original. The moral lesson taught every TNG episode so bludgeoned the viewer I tired of it and stopped watching.

I really enjoyed Deep Space 9, too. It's got a comedic twist, and I just can't get enough of Quark and the other Ferengi. The Grand Nagus Zek, whose mellifluous voice I was sure I'd heard somewhere before, turns out to be played by Wallace Shawn, the "inconceivable" guy from the Princess Bride.

https://www.youtube.com/watch?v=SG_A0IOCfdM

One of the important ongoing themes is the relationship between Commander Sisko and his son Jake, which this article is about:

Deep Space Nine Is TV’s Most Revolutionary Depiction of Black Fatherhood

http://www.vulture.com/2018/01/deep-space-nine-revolutionary...

Here's an interesting interview with Avery Brooks (Sisko) and Rene Auberjonois (Odo):

https://www.youtube.com/watch?v=DnWmATqfebQ

The original is a great place to start, especially if you don’t mind older media. The first 3 original movies are also exceptional. After that comes Star Trek: The Next Generation, which is my personal favorite. If you’re still hooked, and don’t mind a change of pace and scenery (and in both cases, a slow start) Star Trek: Deep Space 9, and later Voyager would be the order for it.