I would start with the movies even though they obviously come later than the series for the reason that they were made to be more mainstream. Maybe start with First Contact and if that goes down well, maybe show them BOBW - as both are Borg stories and also related through the Picard character. I would use this is a good starting off point and take it from there.
More mainstream? What does that even mean? Like, "not as good"?
People are acting like TNG is hard to get into. It isn't. This isn't classic Doctor Who we're talking about here. You don't need to choose your episodes carefully or anything. If the person doesn't like something early but great, like Q Who or Measure of a Man, then they will never like TNG, period. So it doesn't matter what else you show them. But I certainly wouldn't start out of chronological order. Why would anyone do that?
As in the movies were made for fans of the show and also for viewers who have not necessarily seen Star Trek before - therefore less background info/character knowledge is required to watch them - the movies in a way introduce us to the characters and give us an idea of who they are, whereas the series does not. Regarding chronological order - I absolutely would not start with Season 1 as a starting off point - its enough to put anyone off!
