I'd most strongly recommend IX and XII.
IX is the creator of Final Fantasy's favorite. It will provide the best encapsulation and celebration of Final Fantasy as a series -- an equal parts wacky, dramatic, and emotional journey through a storybook world. Its characters are utterly charming, and each one's storyline grapples with its own themes, as well as tying into the game's overarching theme of coming to terms with mortality.
XII is the sole mainline entry directed by Matsuno, which will be quite meaningful to you if you've played any of his games (Final Fantasy Tactics; Tactics Ogre; Ogre Battle; Vagrant Story; Crimson Shroud). It's arguably the most mature entry of the series, employing British theater actors for VA to match the classical tone of its script and localization. It's a political story that's less a character-driven ensemble than previous entries, but delves deeply into themes of war, how it affects both those in power and those without it, and how the former need to listen to the latter. Gameplay-wise, it was hugely ahead of its time with its Gambit system, allowing the player to customize the AI of their party as much or as little as they desired.
X -- let me start by saying I would only personally recommend the PC version, because it is the only version with quality of life features such as fastforward and encounter toggling, in a game that sorely needs them. That caveat out of the way, it's Square's first take at a more linear, cinematic, voiced experience. The characters and story are mostly quite good, and it's worth experiencing, even if that linearity and lack of overworld map detracted from the overall worldbuilding and hitherto "Final Fantasy" feel.
VIII I would flat-out not recommend. It's a mess of a game on every level. Characters are largely bad, story is nonsensical (all the mindfuck of VII with none of the themes, character depth, thought, or payoff), and the combat system is poorly-explained and just broken all around (and not in a way that I personally find enjoyable).
