Okay, I'm going to rank them in accessibility.
FF7: Shows the series' stronger points while not bogging the game down with horrible voice acting. Almost everything is explained relatively well in game, and the materia system is pretty easy to learn. Also, stays a bit more true to what an RPG should be in allowing you to ignore the main quest occasionally. Graphics are still presentable today, particularly when played on an emulator. Lots of the scores pay tribute to FF1-6 and some of the stronger original music too.
FF10: Very accessible, but the voice acting in English (hell, even Japanese) is god awful. Story has some cool moments, but tends to get pretty nonsensical as the game wears on. Also, puzzles, horrible, horrible, half-hour+ puzzles. Other than a few scores, the music is largely forgettable which is a cardinal sin for a jRPG. Leveling system gives... the illusion of choice. Also, unlike most FFs where you can explore a little, this game is rather linear in that regard. There is no overworld map, and when you get your airship you're just selecting destinations.
FF6: Graphics were great for the time, but if you don't like 16-bit graphics, it's going to be a hard sell. The most coherent plot of any Final Fantasy that has one (let's be honest, 1-5 had some pretty bare bones plots). The Esper system can get a little frustrating when you're trying to raise a particular stat, but otherwise it's an okay system. Has some great plot twists and the music is the best in the series.
FF12: It's a single-player MMO. Plot starts out strong, but quickly throws away any goodwill it built with the introduction of Vaan and Penelo who drag the entire game down. Music's largely forgettable and the combat as the game goes on removes you more and more. It's fun the first 20-30 hours, but you're ultimately going to wish the game wasn't designed for you to be less and less involved in combat. On the plus side, however, is it has the hardest bosses in the entire series and they were easily the most fun I had in the game (although, sadly, it's really easy to cheese some of the harder fights if you learned the game).
FF9: By the time 9 came out the graphics were dated and to make up for this Square went full-on chibi character models to harken back to the 1-6 days. Rather than Espers, Materia, or innate powers characters draw new abilities from wearing armor and wielding weapons which means you're going to be hording every piece of gear you acquire. The plot starts out good and fun, although it starts to falter when an antagonist is introduced. Music largely harkens back to earlier FFs. By the third disc, the plot has fallen off a cliff imo, but it was ultimately pretty good up until then.
FF1-10 stick to roughly the same combat style with later ones (if you want) emphasizing speed of entering commands as part of the difficulty.
Post edited July 03, 2012 by TVs_Frank