First Contact (movie) has a bit of a backstory to set up, with the Borg and Locutus.
I thought about a Q Who-BoBW-First Contact marathon as an introduction, but the Borg have more of an impact if other adversaries are introduced first. Imagine how lame the Romulans would seem after being first introduced to the Borg.
And one truly misses the impact of Locutus, if that is one's introduction - Picard being captured and assimilated blew our minds in 1990 because we were so invested in the character at that point.
I have considered DS9 as a way to introduce Trek to the newbees - but which episodes ?
Once again, my argument above prevents me from showing "Emissary" to any noob. Besides, I wouldn't want to spoil BoBW to a noob.