There is no #1 best way to watch it. Here’s my thoughts.
I did not watch the original series with Shatner, I have a hard time watching old crappy TV so I’ll go back and watch it later on in life sometime.
I have not yet watched The Next Generation in sequential order. There’s just so many episodes, and I’ve watched a mixture of them on regular broadcast TV such that I would have to watch it all in order to ensure I had seen them all. TNG is my favorite of them by far, even though I haven’t seen them all.
Deep Space Nine needs to be watched in order. I personally loved this series even though many others did not. I enjoyed the similarities to our society and the developing plot over the seasons. In my opinion DS9 is most like Babylon 5, so if you enjoyed B5, perhaps you’ll enjoy DS9.
Voyager…. well again IMO it’s the worst written series of them all. But I still enjoyed watching it, even if I spent half the episode criticizing Janeway’s choice of action.
Enterprise is the last series produced but the first one chronologically. I absolutely loved this series. To me, it’s everything that Star Trek represents. The only problem in watching it first is that it has the best special effects, thus watching anything else (save the movies) will look pretty corny.
The movies are to me icing on the cake. And half of them are god awful, on par with Voyager’s writing.
Thus my recommendation to you is to start with The Next Generation and work your way out from there. I do NOT recommend watching DS9 without having watched TNG because of the reoccuring characters (you’ll feel more of a connection with them after watching them in TNG). Similarly, Voyager should be left till the end. You could also start with Enterprise then go on to TNG if you want some immediate gratification (such as if you only got into Star Trek via the new movie).
Good luck, have fun! It’s a great world.