Everybody else already mentioned PSP versions being definitive and 3D ones of 3 and 4 being good, and I agree, my 2 cents on games that I played a lot:
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Final Fantasy 1 has two separate magic systems. Original Famicom/NES, Wonderswan color port, and PS1 versions, as well as Pixel Remasters, have D&D style system with spell charges per level. Anyone who played Sorcerer in NWN or Baldur's Gate will understand. GBA & PSP releases changed it to mana system. So pick what type of magic you want, it's the single biggest gameplay change and it's not stated on covers which magic each game has.
I actually enjoyed playing PS1 version as the one that fixed a bunch of stuff and updated graphics without changing magic completely, now you can do Pixel Remaster to get a similar experience... So:
FF1 original, PR or PS1 for old school magic
FF1 GBA or PSP for updated magic
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Steam version of FF4 3D remake has normal and hard difficulty to choose, DS original is ONLY hard so get PC port instead of emulating. 2D version of Final Fantasy 4 was heavily cut down in American SNES release, it's missing half the skills, but was made easier to compensate. The music also sounds really thin and sprites are small as they developed the game for 8-bit consoles. So stay away from original release of 4, compared to, say, 6 where original version is already good enough.
So for 4: ignore SNES, choose any later version depending on which you think looks better, but be wary of DS difficulty. 3D version on Steam is very good and can let you change from normal to hard on New Game+ after getting OP armors and it removes touchscreen gimmick summon and changes a few quest to accomodate. Highly reccomended!
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Finally, FF5 and FF6 never got releases with upgraded graphics (PSP sprites are much bigger and smoother than Pixel Remaster ones), but got botched ports on mobile and PC with redrawn art, and badly-implemented filtering. You can't buy those but they're freely available in obvious places.
The thing with these two Old Version FF5 & 6 ports, they had a modding scene before getting delisted, IMO definitive Final Fantasy 5 version is the old PC port with PSP-style sprites mod on top, it looks gorgeous, and for 6 there's Brave Steel with sprites based on Brave Exvius. Again, better looking version than PR if you can get it to work. BUT both games were good in original form, and they didn't change graphics in FF5/6 releases on PS1 or GBA, just added content so there's nothing wrong playing all games on Gameboy Advance emulator.
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For 3D games there's not much reason to use old versions since you can mod the newest releases anyway. So absolutely pick 8 Remaster, HD version of X, and 12 international system, for non-remake 7 the 7th Heaven tool will downgrade any version anyway.
tl;dr: 2D games each have reasons to play the older versions, 3D not so much.
