I'm a huge original series fan. Yes, it's of its time, but good storytelling is good storytelling. Unless you get particularly twitchy about the sexism that comes with the period (I can't blame you if you do), it's more than worth a watch.
If you want my opinion of the overall best series, I'd say that's Deep Space Nine. But it is ideally enjoyed after viewing at least some of Next Gen, since it's somewhat a response to the optimism of that series. So I do generally recommend going in chronological order.
As to the dregs, Enterprise is the only series I never managed to get through. Picard set up some brilliant ideas in its first couple of episodes, but followed those with absolutely dreadful execution. It's a real shame.
Everything else falls somewhere in the middle. Discovery seems to have the loudest haters, but I'm a big fan, and have frankly never understood the hate. It falters a little in the second season, but undergoes a bit of a transformation in season 3 and 4, which I very much enjoyed.
Regarding the films: all the original 6 are great, with the caution that The Motion Picture very much takes its time (just try to think of how appreciated all the beauty shots of the Enterprise would have been upon release, when you'd have been used to '60s TV production values), and The Final Frontier is very cheesy (more like TOS itself than any of the others).
After First Contact, the Next Gen films take a bit of a dive, ending on a very sour note with Nemesis.
And the less said about Section 31 the better.