TOS #3: Where No Man Has Gone Before

This "first episode" is really the second episode, if you count the pilot. It has the prototypical Barkley character, lots of exploding bridge panels, a marooning, a mining colony, love stories, a discussion of Spock's human blood, and 3D-chess.

The episode is about absolute power corrupting absolutely, but the interesting twist is that it's also about monotheism. You could also argue maybe it's a feminist episode, because it's about how if men think they are more powerful than women, they die.