I definatley don't like how the article says: ".... and one you should probably avoid." That should be taken out, in my opinion. I would personally put FF12 as the worst, because despite how much I tried to like it, I could never bring myself to play it very far.
My best is one a lot of people seem to have issue with, which is FF13. This is the *only* FF game that I was seriously very sad that it ended, and I wanted more. Part of this, is I just loved the characters and the unique battle system. In fact, I'm sure my opinion is going to shift towards 13-2 as my favorite because having played the demo - I can tell they have listened to player feedback. The game also had a very engaging story, and despite the linearity in the beginning... I don't see how anyone could say it was not fun.
Favorite Ones:
-Final Fantasy XIII
-Final Fantasy XI
-Final Fantasy IX
-Dissidia FF (this was super fun)
Worst:
-Final Fantasy XII