I loved some of the characters on Deep Space Nine but didn't care too much for the captain or his family stuff. I loved the Bajor planet story and how the people lived such a peaceful life until they were taken over by the Cardassian's.
I had the biggest crush on Dr. Bashir and looked forward to his interactions with Garak, the tailor, and Quark. They could get into some messes.
I also liked how Worf's story played out and the O'Brians. They all ended up on Deep Space Nine and had more story.
I enjoyed Dax. How she had this little critter living inside her that had been alive many many lifetimes. When it joined with her she gained all the memories it had of each and every host it had been with and each activity they had done. So she was proficient in many games, sports, languages, cultures, etc...and yes, she kissed a girl and liked it...lol. The woman was the mate/love of a past host. Her feelings for this woman were as strong as the mans because Dax had them inside her too. It was a complicated and fun combination for this character.
Odo's character was one of the most interesting to the whole plot of the wormhole. He was a shape shifter and had no recollection of where he came from or what sort of being he was. He was often awkward and insecure. But he was an awesome security chief.
I guess my favorite story was that of Major Kira. She was supposed to follow her family traditions but ended up being a soldier to defend her planet. She grew and became a great leader to her people. She wanted to be faithful to her traditions and morays but they were so different now that they had been shoved into the rest of the galaxy by the popularity of the wormhole.
Then there are the Ferengi's. What a race of people they are with their rules of acquisition. I enjoyed seeing Rom grow and turn the tides for his whole race of Ferengi. He actually is the first Ferengi to join Starfleet after causing Quark as much trouble as possible of course.
I hope you'll give it a chance, it's actually one of my favorite series in the whole Star Trek world.
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I also liked Voyager. It had it's own story that was pretty independent of the whole Star Fleet headquarters and stuff. They got kidnapped to another quadrant of space, so far away it would take them lifetimes and lifetimes to travel back home.
Some wanted to give up, find a suitable planet, colonize it then live there, and others wanted to try to get back. They had little hope of returning home so they were a set group of humans on a ship with limited number of other humans to "hook up" with. The couples that form and relationships that happen are often interesting and challenging. They do get home in the last episode and are happy to finally on Earth again.