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.
I'm a HUGE fan of TMP. But I don't feel the same way. For a hardcore Trekkie, it's perfect. For someone who doesn't know Trek, it's to much at all once. It's like introducing someone to Indian cuisine, and choosing the hottest, spiciest curry you can find. It's an overload.
I was introduced to Trek through TMP, and I can honoustly say that, even though I love it to death, had it been the first Trek I ever saw, I would have changed the channel.
There's also the fact that the whole first part of the movie is about getting the old gang together and reuniting Kirk with the Enterprise
--all of which works if you already
have an emotional connection to the characters and their history. But will mean nothing to newbies.
Ditto for all the scenes establishing that Spock is oddly aloof toward his old friends, even by Vulcan standards. Again, Spock's brusque manner upon meeting Kirk and McCoy registers if you're already familiar with the characters, but a newbie is likely to be puzzled when Kirk or McCoy or whomever are somewhat taken aback by Spock's attitude . . .