Start with the latest movie (Score 1)

The 2009 Star Trek movie was brilliantly done, and worth watching over and over. For someone who's never watched anything Trek, it's a nice high quality introduction to the characters. Use the movie to make them fall in love with the characters before exposing them to the melodrama of the 60s show. Once someone is hooked, they can watch just about anything Trek... even Deep Sleep 9!