In terms of starting
Old school wise = FF1 and 2 Dawn of Souls (GBA) or FF1 Anniversary/FF2 Anniversary on PSP
2D wise = FFIV or FFVI (go retro SNES or PSX versions - avoid all others except for the PSP version of FFIV)
3D wise = FFVII or FFIX
Or you can try FFX/X-2 HD but warning it is linear in design dungeon wise and such - not that it is a issue - the presentation, OST, characters and gameplay system make up for it.
I would recommend XII if you loved MMOs but dont want to spend hours and subscription monies. XII was drop dead gorgeous (when I bought it back day 1 ).
XIII/XIII-2 (cant say much about LR since I dont own it) are pretty good although I enjoyed XIII-2's gameplay system especially with the use of monsters as allies although I felt the cast of characters were weaker in a sense although FFXIII's character cast isnt so praise worthy (aside from Sazh of course).
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In comparison I started the FF series with FFIV back when it was known as FFII when I first rented it in 1993. My first actual purchase of the series wouldnt be until 2003 when I bought both FFIX and FFX when I bought my first playstation: PS2 :O - but I did play FFIV, FFV and FFVI beforehand the SNES versions of course.
Oh ya here's my current FF Score rating list
Final Fantasy I & II Dawn of Souls (GBA): 83
Final Fantasy I Dawn of Souls (GBA): 82
Final Fantasy I Anniversary (PSP): 85
Final Fantasy II Dawn of Souls (GBA): 83
Final Fantasy II Anniversary (PSP): 85
Final Fantasy III (NES): 80
Final Fantasy IV (PSP): 94
Final Fantasy IV After Years/Prologue (PSP): 88
Final Fantasy IV Complete Collection (PSP): 91
Final Fantasy VI (SNES): 95
Final Fantasy VII Crisis Core (PSP): 93
Final Fantasy XIII (PS3): 88
Final Fantasy XIII-2 (PS3): 86
Final Fantasy Dissidia (PSP): 100
Final Fantasy Dissidia 012 (PSP): 96
Final Fantasy Tactics (PSX): 94
Bravely Default (3DS): 95
^ There's other games I finished in the series - but I only started rating after 2010 but ya these are all the FF games I played starting in 2010
Don't listen to Basil, he didn't put the best FF in there, which is 8. So he's automatically wrong on everything.