@Beware: While I do think VII is a phenomenal game, if we're giving a complete newcomer a taste of what to expect franchise wide, I think X, III, IV (their remakes mostly) can give the good sample of what the series can be about, how it feels to play more or less, while still being great games by themselves.
III has a very fun class system, is lighthearted enough with a simple yet enjoyable story that works as a good first step to enjoy yourself, let yourself be carried away, before tackling the more complex elements in other more story heavy games. IV has that old school balance of everything FF-ish, different classes but customization allowing for strategy, a simple yet lovely story, with drama and turns in reasonable doses, character with their arcs and proper development in a reasonable focus etc. X as Pachi and the video mentions has a lot of newcomer friendly elements, it mixes very well the classic fantasy feel with the technological bits of later entries, the story is more complex but aside some twists it's not convoluted nor too heavy handed, it looks great and the atmosphere is incredible even today.
While futuristic settings are common in FF today, the Cyberpunk aesthetic is not so much, and while only Midgar has it, it can be off putting for those expecting a fantastic world. While I do think the atmosphere and setting of VII still works out today, the graphics are dated and nowadays many players do pay a lot attention to graphics. The story can be rather convoluted if you haven't kept up with other materials of the Compilation (whether Cloud was real or not, the Sephiroth Clones in Nibelheim, the ending, among other things are rather ambiguous in the game itself). The combat Zig-Zags, if you like ATB, then it's perfectly serviceable, but if you're not too sold on it or expect it to have havier customization or complex strategy like the newer Persona games or the Bravely series, then it could be off-putting.
There's also the whole "This is the best game EVUR!" and "FFVII is OVARRAYTD!! stigmas that can stain the perception of the game, mainly planting expectations too high or putting a cynical filter on the player that may affect the entry on the series as a whole. Which I think could be better avoided if they person already has an opinion by themselves before tackling VII and having their own experience. I think VII is better reserved once a player has realized they do like FF and wants to experience the twists and turns VII offered once they have experienced the essence via other games.
I'd speak for IX as well, but I remember very little of it since I only played it once...
