Unless your wife likes 60's stuff, I'm not so sure I'd start her off with TOS. I love the show and grew up on it myself...but for a first time viewer who is not attached to Trek yet and couldn't care less about Kirk, Spock and McCoy at this point in her life, I think the 60's look of it might be a bit distracting. It's obviously worth airing for her once she's into Trek...but I don't know as I'd start with it unless she likes retro stuff like scifi movies from the 50's and 60's, etc.
However, if you are just determined to start with TOS, I'd suggest
The Menagerie. That's a story that girls like, and doesn't require you to know anything about Trek because the chief character in the episode is not even a regular! It's very self-contained, that episode.
IMO, the best movie to start out with, if you are gonna start with a movie, is
First Contact. It's the only TNG movie that is really good, it's not dated at all, and it's a fun and exciting story that takes place mostly outside the 24th century, so it doesn't require much backstory except for an explanation of who the Borg are. Forget about
TWOK or
The Search for Spock. At this point, your wife doesn't CARE about Spock, and so the best part of those films - the emotion involved with Spock's death - would be completely lost on her (same goes for the TNG episode
The Inner Light, by the way - it plays alot better to a person who has actually come to give a rip about Picard. Same with
The Visitor - one of the best episodes of DS9 and an episode that girls generally like, but it's alot better for someone who has actually come to
care about Ben and Jake Sisko).
If you want to get her into a series, I would actually suggest either DS9 or Voyager, depending upon the sort of TV viewer she is. If she likes serialized stories with lots of drama, character development, intrigue, suspense, and stuff, I'd say DS9. If she likes lighter entertainment or 'shippy stuff, I'd opt for VOY.
Both of those shows have aged well visually...and DS9 in particular is alot more like many shows on the air today - shows that have absolutely nothing to do with Trek or scifi.
Remember - your first shot at getter her interested will be your best shot at getting her interested. Make sure you don't show her what YOU like, but what you think SHE will like.
If you hook her, you can always show her what you like later.
