Final Fantasy III is an interesting game in the series. For the majority of non-Japanese speaking Western players, the 2006 DS release was the first chance to experience the game, even though it originally appeared on the first Famicom system in 1990. There's not much to the story (with even less than its predecessor) and the remake had to (try to) expand on the main characters' backstories a fair bit in order to give them something resembling personalities.
The overall themes in Final Fantasy III are very similar to those of the first game. Although they add a few additional quirky elements like shrinking down to save a tiny village, they also introduced an important concept that would be repeated throughout several later games: the main antagonist's wish to be an immortal deity.
What stands out the most about this entry in the series is its battle system. Final Fantasy III has a much-expanded job system compared to the series' first entry, including well-known classes like the Sage and the Ninja (though in later iterations it's mostly found in spinoffs like Final Fantasy Tactics). Overall, it makes for a much deeper experience, which helps compensate for the fact that there isn't much else in terms of depth on offer here.