The first game I'd played in the series was X after being recommended it by a friend. I really liked JRPG's and I hadn't even heard of Final Fantasy, and I think I'm the only person EVER to have that happen (in my defence, I wasn't a big gamer back then).
So naturally, I was blown away by the magnificent story. Spurred on by that, I rented XII when it first came out. Absolutely loathed it. Looking back, I don't remember much about it, but I couldn't stand the characters, the gameplay, everything. Because of my disappointment, I bought VII for the PS1 preowned. The second disk didn't work, so here I was, halfway through a story and not allowed to continue. By now, my rage for the series was so much that I just abandoned it completely.
Until VII came out on the PSN. I bought it without a second thought. Completed it, and finally understood why everyone said it was the greatest FF ever. It certainly was in my eyes anyway (even if it was a bit dated.)
I also bought XIII simply because I thought it'd take a good time to complete. It didn't, and I (like many others) really didn't like the game. The music was the highpoint of it for me.
Eventually I bought VIII, IX and VI (in that order) on the PSN. I've yet to play VI but I've completed VIII (just last week in fact.) Long story short. I absolutely adored VIII. I loved the characters (Zell and a few others excluded,) it took a while to get used to the gameplay, but I really enjoyed it when I did and the story was really nice.
Short version:
X - My introduction. Loved it aside from the dodgy main character.
XII - Loathed it.
VII - Absolutely loved it. It looks quite dated by today's standards, but still really immersive and enjoyable.
XIII - I suppose it's alright, but not as immersive as the others.
VIII - My favourite. Loved everything about the game.
IX - Can't say I'm too far in it but I prefer the more realistic ones.