I like none but XIII, and even that I'm only slightly fond of. However, I do really, really like the story in XIII, and XIII-2 has a nice story as well, and it's a lot more fun. I'd start with that, I guess. The older ones are all complete s***, if you ask me.
Mai waifu: http://img62.imageshack.us/img62/3729/maiwaifu.png
Most people in the world's fav is 7. So personally I'd suggest you start with 7. It's graphix are terrible, so if you do another one 1st, you might find it unbearable. But if you do it 1st, it might be your fav also. Also, it has many secrets and missables, so you'll need a walkthrough.
Another good one to start with would be 12. It's fun, has average difficulty, better systems than 13, great graphix, good story, enough side quests, enough but not too much customizability, few missables.
Tactics Advanced (if you have access to it) is an easy, light one. The tactics games have very different battle systems from the rest (chess-like battles), but Tactics Advanced should get you well acquanted with the things that are common occurances in the series, like the spells, items and job system. Though you can royally mess up if you discard an important item and save, leaving the game unfinishable, meaning you've no other choice than to restart. However, if you have access to a gameshark or some other cheating device, you can fix it, or search the forums for a list of safe-to-discard items.
I started with Final Fantasy 8. And after playing 14 different ones, it's still my favourite. But most people seem to hate it. Recently replayed it, and it was rediculously easy. Play this if you want an easy one.
XIII veers quite a bit from the other Final Fantasies. Though they still have the traditional elements like the spells, jobs and such, it's still quite different. Can't explain. So wouldn't recommend starting with 13. Though on the bright side, it has no missables (unless you do something silly), and no hidden side-quests. You can't mess up custimization either. But the game is one of the more difficult ones.
Oh yeah: One common occurance in final fantasies is that the enemies grow stronger much faster than you do. So you often have to stop and grind some experience to catch up. In 5, this is a big problem. In 12, sadly, it's also a bit of a problem. In 13 it's almost no problem, in 13-2 it is no problem at all. In 8 the enemies grow with you; your main char will likely outlevel your other characters, and the enemy will be somewhere inbetween.
I agree with D_G. If you're going to play 7, play it first, so that you aren't disappointed by the graphics later. (Or buy the recent PC rerelease of it and mod it to the nines, but that's a significant time investment depending on your download speeds.)
I personally think 10 is a good starting point for newcomers. It's pretty, has a fairly simple battle system, even if lots of people hate the sphere grid levelling system, and has a d. good story, possibly the deepest one of any FF title because of its focus on the value of life and death. It's not my favourite, personally, but I think it's one of the most accessible.
Of the classic, classic games, I can't help but stick in a rec for FFIV. My favourite character cast of all. But 9 is also a great example of the classic RPG style, and that one is just flat out fun in its outlook. Its sole purpose is to be fun and have fun along the way, which is possibly why it's often not taken seriously.