TL;DR
I really like 5, 6, 7, 8, 10, 10-2, and 12. All are compelling in their unique ways. Look them up, play what seems interesting to you.
Most culturally relevant
FF7 - your party are ecoterrorists trying to stop a megacorp from literally sucking the planet’s lifeforce dry. No further comment.
Best overall
FF10 - has a compelling story with some information drops that totally change your perspective on what’s going on, a great combat system, interesting character progression system (the sphere grid), and - besides the temple puzzles that I hate with a passion - is very fun.
Best combat system
FF10 still. Turn based where your moves get executed immediately after you select them is the best form of turn-based. It’s why I like Shin Megami Tensei so much.
I’m very partial to 12’s combat system as well, wish I could find something like it. In 12 you program your party members based on triggers. The game is less about choosing actions and more about making sure your party can react appropriately to situations. You might have to change the programming in the middle of a fight because some subtle interactions or the right conditions get your characters stuck in a loop. Very fun once you get them set up. Just move your party around with the joystick and watch them fight everything they see. I love it.
I actually don’t like the ATB system all that much, but 10-2 is the most fun iteration of it. Also I love a lot of the games that use it but that’s despite the system.
Most engaging character progression system
Several answers:
Job system
Characters equip jobs and can sometimes learn skills to equip while being other jobs. FF5 and FF10-2 are sadly the only main examples of this. FF3’s job system exists but is definitely half-baked. The Tactics games also use job systems.
I think 10-2 is one of the most
Junction System
In FF8 you equip spirits - called Guardian Forces or G.F.s for short - to your character that then give them actions, stat ups, and junction points. You equip a magic spell in that junction point and get a stat boost. Or if you junction to your defenses or attacks, you can become immune to things and inflict statuses with your attacks. I say the mechanics are fucked in this game because you need to engage with the Junction System. Enemies have level scaling and will out scale you if you just rely on level grinding. Which is a valid strategy in any other FF game (part of why they are generally low difficulty). But it is very fun if you go in with an understanding of what you don’t want to do based on how mechanics work.
Zodiac Job System
FF12 not only has a great combat system, but it also has interesting character progression decisions. Every character gets to dual class. Dual classing is always so interesting in games, having 6 characters to do that with rules. Think you made a mistake? Reclassing is easily available. The license board system for unlocking things for your characters allows for some interesting decision-making when resources are limited early on, but I don’t like how slow reclassing is because you have to unlock every individual node.
Sphere Grid
FF10 has a system where combat does not earn you XP. It gives you movement points to spend to move around the sphere grid. On the sphere grid are nodes that unlock abilities, spells, increase stats. Each character starts on a pretty well defined path, but once you finish their path? You get to decide. Think Tidus needs to hit even harder? Take him down Auron’s path. There’s also items that let you teleport around the grid or unlock nodes from afar. Yuna needs one damaging spell? Boom, Blizaga since Lulu had already been there.
Best story
FF6 - I like the split narrative and the successful attempt to make it an ensemble cast in a sprawling adventure. Very memorable villain, interesting storylines, and the second half trying to find your lost party members after you got split up (just a small apocalypse, no biggie) is the most compelling part of the game. When I was younger I thought FF6 was the best in the series (I had only tried 1-6) and I never even got to the best fricking part! Oh man it’s so good, I love 6. I also think that the games where magic isn’t readily available to humans are more logically consistent and therefore more compelling. Magic abilities suddenly solving problems can feel like a Deus Ex Machina and are wildly inconsistent, which makes it hard to take any stakes seriously. (Oh I’m looking at you, 4)
My favorite?
FF6 is a beautiful piece of pixel art and has such a good story. Amano’s concept pieces for the game are among my favorites of his work. The music is beautiful. Especially in the Pixel Remaster version where they can use real double bass pedals and a drum kit for their prog-rock as final boss theme. The 14 party characters are unique and memorable and you are encouraged to use all of them. The final dungeon makes you form 3 teams of 4 who all have to explore different parts and fight different bosses. It was very engaging and forced me to split up Terra and Celes. Figuring out balanced parties required some thinking and made the fights fun even that late into the game. The character progression system is limited since everyone is their own character, but you do get to equip magicite to characters to teach them spells over time and get to make choices there.