Note: I am referring to the NES version

I know what you're thinking: "Just play the other games". Trust me, I've tried. They don't have the same feel. Maybe the first one can compare but the others just feel too wrapped up in the story and forget to establish an amazing atmosphere.

Things I liked: Your party wasn't given backstory and/or significance. They were blank shells that you could project anything onto. They were experiencing the story just as you were. They had no internal thoughts, goals, morality. I tried to play 4 but I can't connect with any of the characters and the atmosphere is dreadfully bland.

I also enjoyed the fact that you could make your party into anything you wanted. You could have variety in how you build your group from the start rather than trudging through a bland narrative to acquire a certain class.

if you liked the job system in ff3 you should definitely play ff5, as it expands upon it and opens up a ton of possiblities as far as an rpg with a minimal story or characters, i guess just other early jrpgs like final fantasy 1 and dragon quest 1-4 (ff2 is p story intensive for its time so not so much that one) and bravely default for a more modern take on the job system

I'd try the Etrian Odyssey series. It's pretty lackluster in character development if I recall. As crash said, FF5 is a def must. Bravely Default is fairly story heavy, I found that Dragon Quest 8 is more grindy and has less character development (some of the scenes are completely optional for character dev.)

The DQ series uses weapon (skill) trees so you can actually customize your characters as you choose. The GBC ones that were released are probably more up your alley for FF3.