I think it's funny that Devon mentioned showing this movie to non Trek fans as an introduction, because I've done literally that!
My proudest moment as a video store clerk was when a 10 year old boy approached me asking about renting "the first Star Trek movie." I showed him to "Star Trek: The Motion Picture" but advised him that "Wrath of Khan" was far superior. Weeks later his mom shows up and asks for the next Trek movie (by that point he had been through 3 and 4). She told me that ever since he rented Khan their dinner table was nothing but arguments over Star Trek vs. Star Wars between this boy and his brother. Sorry exhausted mom, but that made my day. By far best thing that ever happened working there.
It would be impossible for me to divorce Trek from my view of the world, and the impact it has had on my life. That being said, even my friends who don't like most Trek agree that "Wrath of Khan" is one of the best sci-fi films of the 20th century. I would pick it to represent Trek, and sci-fi as a genre, over my personal favorites. It has action, it has heart, and it has tension.
P.S. We do exist, those of us who like both Trek and "Working Girl." Although I registered now to vote for this film, I will happily log in and defend "Working Girl" and it's Canonness if it goes under the boot.