|You do not want Buffy looking at you this way.|
The challenge today is how to spread the word to those who still don't know how great this show is.
The trouble with showing them the two-episode Pilot first is that it's not as artful as the show gets later on, and it's shot in 16mm (grainy) on a shoestring budget. They do amazing things to work around the budget limitations (such as using placement of different colored lighting and key lights to create the sensation of depth to overcome the "flatness" of 16mm film stock), but production values soar later on. And people care about production values, even though few even know what the term means.
The trouble with showing them anything else is that the show is so serialized that showing people anything later necessarily involves spoilers--and having to explain a lot of things that would otherwise fly over their head. You'll have to make a judgment call about what would suit your friend best.
For the art film crowd, "The Body" is the obvious choice. That's also good for someone who isn't a big fantasy/scifi fan, since there's so little of the supernatural in the episode. For an Avengers fan, maybe "Hush," which is a tour de force of screenwriting after all. For a Twilight fan, maybe "Buffy vs. Dracula" would be both appropriate and something of an antidote. For a Glee fan, the Buffy musical episode "Once More with Feeling" is the obvious choice.
I like lots of current shows, especially Orphan Black and--though it may be losing a bit of its mojo--Dr. Who, and even my favorite guilty pleasure, Vampire Diaries. But Buffy had Whedon and Gellar. Whedon has never had a vessel as perfect for him as Sarah Michelle Gellar (though Avengers' Black Widow/Scarlett Johansson is a solid second, deserving of her own backstory film), and Gellar sure hasn't had another writer/director like Whedon--she's done nothin' but clunkers since. The two together in Buffy was and remains a uniquely fruitful collaboration.