Georgie_Leech said:
You might consider trying Paper Mario: The Thousand Year Door. Follows the basic premise of a JRPG (Here's your character, go engage in turnbased combat until the enemies are gone and you uncover the plot) and is really quite fun and polished while doing so. Maybe not a "traditional" JRPG but you'd likely have fun with it nonethelesss.
I second that. Pretty much all the Mario RPG games (both the console and handheld ones) are a good time. They're very polished and well put together/thought out, but they don't take themselves too seriously, and they're some of the few genuinely funny games out there.
Speaking of things on the GameCube, I was pleasantly surprised by how good the Baten Kaitos games were. I had as much fun with them as with most Square games (and more so than the newer Square ones, which I haven't liked as much as their older stuff). Despite both being loooooooong games, they kept my interest the whole way through, and while I figured that the "you're not actually one of the characters in the game but their guardian spirit" angle would be a gimmick, they actually took pretty good advantage of it in terms of what it allowed them to do from a storytelling point of view.
As far as older Square stuff, there's the obvious stuff everyone always says like the FF games and Chrono Trigger, but outside of FF6 and FF7, I'd say I had more fun with Chrono Cross, and for the more actiony side of things, Secret of Mana and Legend of Mana.
Most stuff I've played from the Tales series (which isn't too much) has been pretty entertaining, too.