Haha! This is one of the hardest questions to get a decent answer from.... You can pretty much guarantee that II, III and XIII will be taken out of the equation early on...
XII is usually not reccomended as first because it is so different... That's not a bad thing, it's a very good game, but it's usually better to experience one of the earlier ones first.
Now you have 2 catagories:
The early games:
I
IV
V
VI
and the later games (once they hit the PS1 onwards)
VII
VIII
IX
X
Now the fans are split into 2... usually by age. I am in my mid 20s, and I was of the age to enjoy FF games when VII came out. I naturally fall into the catagory that you should start with one of the later games, as I did, and I still enjoy them the most.
People who grew up with the early games tend to favour them for the same reasons.
People who are younger I find seem to split. They don't have a nostalgic tie, so they tend to advise on which they started with too... or maybe enjoyed the most?
So my personal reccomendation... from looking at them all (yes with nostalgia goggle enabled) would be
FFIX. It has a relatively simple set of mechanics in terms of having characters with abilities and clothing (All characters are preset for differet jobs. There is not a blank slate like with a lot of the older FF games.) This means that you can focus more on the story and characters, which I find are better presented than some of the other games.
The cartoony graphics worked for me too, with the vibrant colours and great atmospheres! It was the last game before everything became rainbow coloured sparkly things (seriously... look at everything from X on... it's strange, but they put it everywhere!)
It also had (IMO) the best optional sidequests, with decent rewards, that didn't feel like a chore! (Although I have played Chocobo Hot and Cold until my thumbs hurt!)
If you prefer games for mechanics and strategy, over characters and story, I would reccomend FFV. I liked the job system quite a lot, and would often change my team to new strengths and weaknesses to test it out... kinda like a pokemon team! Unfortunately... also like pokemon, this took quite a lot of grinding... but so worth it!
EDIT: Oh damn... I didn't even consider FF:Tactics!! Those are the games, bar FFIX, that I have put the most time into! I have played War of the Lions, Tactics Advanced and A2 loads! They are also great for mechanics over story, and have actually quite deep gameplay. The only issue I have with them is that you need to plan ahead to develop your team. You need to know what jobs and abilities you want way further down the line so you can get the prerequisites... and the problem with that is that you don't neccesarily know what you will need until you find a boss that you are stuck on indefinitely! And have to restart... Then again, as the battles are the focus of the games this isn't a huge issue anyway!
