No, much of TNG was made in the stand-alone episode way. I think the plot arcs begin in the... fifth season? I'm not sure, but it's pretty far in. TNG improves by a lot in the fourth season, and I really don't know much about the other series. The new movie is fun, but kind of light on actual Star Trekkiness. More of an action movie set in the Trek universe than an actual Star Trek movie. But movies being what they are- a self-contained three-hour plot line, I doubt you'd find what you're looking for.