I have a coworker who loves Voyager. She told me that she has been watching Star Trek since the very beginning (I believe her,) and that Voyager was the show she had been waiting her whole life to watch. She would watch it with her daughters, and used it to encourage them in science, math, military, etc.
My personal favorite is TNG. I love everything about it, and it was one of my great escapes as a child. That background thrum of the engines makes me feel at home whenever I hear it, and just thinking of the carpet in the corridors and bridge and turbolift makes me smile. Clean carpet, soft steps, traction. I love how the main crew are like a family; it is almost like The Waltons sometimes. I love the utopian vision of Starfleet and the Federation.