HL2 is easily the best choice. Especially prettified with the FakeFactory Mods. The game is still the epitome of the modern shooter, which is a bit sad actually. It has a wide spectrum of gameplay, varied level design, a strong narrative that ties everyting together and on easy it's not that difficult.
Recommending DOOM must be joke. The game looks like ass - and yes, contrary to the Escapist-meme, graphics matter. At least a bit. It's also run-and-gun only with no further gameplay mechanics, has a dead non-interactive world filled with only enemies (completely stupid ones at that) and generic level design (a.k.a. arbitrary sequence of hallways and rooms). How do you expect people who know more complex game design from ANGRY BIRDS to appreciate the genre of FPS if you deprive them of all the evolution it took? You wouldn't try to sell the idea of a car by making people drive the Model T.
I've been playing BLACK MESA lately and it is ultimately disappointing, if nostalgia-invoking.
Level design and gameplay from 1999 just don't cut it anymore. Been saying to a friend of mine that the dream of introducing a new generation of gamers to Half-Life didn't come true, because they will see a relatively modern looking game and judge it's lacking gameplay in comparison with contemporary games, where even third rate shooters are now doing everything HL revolutionized 13 years ago, and label it a hype.
The furthest back I'd go, for the value of being different, is NO ONE LIVES FOREVER. This is one of the very few shooters that didn't take itself serious. It had lots of ideas, lots of COLOR and was fun to play. So people who are reluctant to try shooters because they think of them as muddy brown, violent and written for 13-year-old boys, could be intrigued.
Of course, if a friend is a fan of a particular fiction genre, that could play a role as well. MAX PAYNE was a film-noir, FEAR had horror, DEUS EX: HR for the Sci-Fi fan, DARK MESSIAH for the fantasy inclined, RED DEAD REDEMPTION or CALL OF JUAREZ for the wild west...