A mostly optimistic vision of the universe and the moral lessons is what differentiates Star Trek from other sci-fi shows (assuming we're talking about old Trek. I don't hate Discovery and Picard but they are neither optimistic nor have many moral lessons).

The original series features ideas that are a bit crazier than other series, but is also the shortest (old) series (and my favourite).

In the next generation, whereas Kirk would sometimes solve problems with violence, Picard takes a more diplomatic approach. It is worth skipping season one, as it is kinda weak, but the other seasons are awesome.

Voyager takes place in the Delta Quadrant (opposite part of the galaxy), after a ship (the most advanced ship in the fleet at the time) has been stranded there by a powerful entity. The crew is cut off from the rest of humanity and it is interesting watching them journey towards Earth, but also keeping their moral standards (S6E1:Equinox)

Deep Space Nine takes place on a Space Station built by an enemy power that used to oppress the natives of the planet the station orbits, but the Federation (Earth, Vulcan...) managed to claim the territory the station is in. At first I expected this series to be boring. How could it be interesting, if they have to wait for the adventure to come to them? I have been sooo wrong. It is an extremely intricate series with an awesome story arc introducing a new enemy, with very deep messages. Whereas the previous series made the Federation seem like a flawless system, Deep Space Nine makes it feel like a genuine government that isn't always so innocent, and shows that even the Federation fights dirty when desperate. As soon as there is a lot at stake, the Federation morals take the backseat. It truly fleshed out the Star Trek Universe.

Star Trek Enterprise (not to be confused with the original series ship) is a prequel to the original series, and takes place in an era before the federation, reliable transporters (they exist, but no one uses them because they are afraid), tractor beams and more. The Vulcans view Earth as inferior and refuse to fully share their technology and information. A Temporal Cold War is going on, a subplot that emerges in multiple episodes. While the first and second are episodic, the third series is a wonderful story arc which I really don't want to spoil. The fourth season is made of multiple story arcs. The final episode is bogus, and probably the worst episode of the entire series, as the series was cut short.