Don't know if this will help or not, but I think you should expose yourself to the whole franchise and here's why:
If you're going to watch the original series, you might as well watch all three seasons. It started the whole thing and should put any misconceptions about Shatner at bay.
Focusing on The Next Generation, season one (with the exception of the first episode) pretty much stinks as far as action and story go. I'd recommend the last few seasons because the characters are much more developed, and the stories are more enjoyable overall.
Voyager would be a good one to start with as well. Aside from Deep Space 9, (

which I think stinks on ice overall) Voyager is the most distinct of the entire franchise (in my opinion). I highly recommend it.
As for Enterprise...a lot of people don't like that show because it's set as a prequel to the original series, and to be creative and fresh the writers sometimes didn't follow the established history of Star Trek canon. I thought it was a decent series overall, but it shouldn't be a primary focus if you're trying to learn and appreciate Star Trek.
I could tell you some of my favorite episodes of each series, but it might help to tell me what kind of stories you're into first.
PS: You should at least watch the series premiere and finale' of each series. The movies are nice to explore too, because they're a lot more jampacked than episodes could ever be....