I'm in minority, but still...
I think, the best beginning is The Motion Picture. The reasons, why:
1. Gene Roddenberry and his vision.
2. The best cinematography and the best music.
3. The best example of what is the Star Trek villian should be.
4. The best basis for discussions and questions to Trekkies
TMP is the best presentation for Star Trek world. This movie can lead to good discussion and arouse interest to other movies and shows.
The problem is, our hypothetical layman doesn't care about Roddenberry's "vision" or what a Star Trek villain should
be. You want to show them what Star Trek is,
not what it should be.