FF4 is considered a classic, but not a favorite among Codexers. It's short, linear, and has no character building to speak of. If you're looking for a quick storyfag romp though, it's a pretty decent introduction to the series, to whet your appetite for the classics like 5, 6, 7*, 9*, and 12*. FF4 is one of the few games I've played where the romance isn't sickening since it's pre-established, and is between 2 adults rather than a coming-of-age teenage sob story, even though she plays the damsel in distress part more than once.
* - There's a small debate about how 'classic' these really are, but the positive voices mostly outweigh the negative, just like the positive aspects of the game mostly outweigh the negative. 9 is probably the one I would be most hesitant to recommend to you from a storyfag perspective since it's a bit tongue-in-cheek, and never really takes itself too seriously. Soundtrack is on point, and it's the swan song for the classic ATB system. 12 is the most conflicted, but it's my personal favorite, though I will say take my opinion with a small grain of salt, as I'm a self-admitted Yasumi Matsuno fanboy. Most of us here are to a degree, though.