Re: Which movie would you use to introduce someone with Star Trek?
Most everyone I know who aren't Star Trek fans will watch Star Trek 4, it is a lighthearted place to start.
...though, when I first read your excellent thread idea, the first thing that popped into my holodeck addicted mind was series...depending on the age...for younger, I would start with TAS...for older, TOS...I know your thread asks for movies, but maybe something else to consider...
"If man is to survive, he will delight in the essential differences between men and between cultures. He will learn that differences in ideas and attitudes are a part of life's exciting variety, not something to fear" Gene Roddenberry