Well I can't speak for GBA but I can suggest a few for PS1.
Get the elephant in the room out of the way and say FF7, but in my opinion theres better ones.
A few of my favorites from ps1 era are:
-Chrono Cross: Sequel to Chrono Trigger on the SNES, but still playable even without playing Trigger because most of it that relates to the 1st game are small references. Also has an amazing soundtrack, amazing story, and a multitude of characters (most are pointless though). I highly recommend.
-Wild Arms: This game is awesome.
-Wild Arms 2: Refer to Wild Arms.
-Legend of Dragoon: This game was my childhood. It has some pretty stereotypical jRPG elements (bad guy with silver hair, spikey haired main character, each character represents different element, etc.), but even with those things it is still an amazing game.
-Lunar Silver Star Story: To be honest I don't remember much from the game, but I remember liking it a lot.
-Final Fantasy 8: Not anywhere near my favorite of the series and I absolutely hated the draw system, but the characters and story are cool so it may appeal to you.
-Breath of Fire 3: Again, I don't remember it much other than liking it. Plus you start off playing as a dragon.
-Xenogears: Never played it but have heard good things.
Well thats all I can think of from PS1, sorry I'm no help on the GBA though.