Valkyrie Profile: unique gameplay for a JRPG, dungeons feel like 2D platforming levels with some puzzles, and combat is quite original and fun, cool art style. There is a PSP version, but people claim it's inferior to the PSX one.
Star Ocean II: it's a bit of a mix with sci-fi/Final Fantasy elements, allows a lot of customization through skills, items, etc., gameplay reminds of Tales of. Usually overlooked. There is also a remake for PSP if I remember correctly.
Xenogears: the plot is cool and intricate, but storytelling is not so great (second CD is just mere exposition, and it drags often on the first one); it has two combat systems, one on foot, another for the mechas, but both are quite simple yet not bad; go for it right now if you liked Evangelion. A nice experience overall, but not for everyone.
Threads of Fate is quite bland in my opinion. If you're looking for a more action-packaged JRPG, Brave Fencer Musashi is way more fun.
Also, if you're going to try action-rpgs, go and check the first Alundra, which is probably one of the best games in the genre, and it will look lovely on your PSP. I finished it on the PSP too and it became one of my favourites of all time.
I couldn't beat the first Digimon World since I got the PAL version, but despite that it wasn't such a memorable game. I completed DMW3 though; I look at it with tender eyes but inside me I know it's only pure nostalgia since the game it's not quite good; moreover, running it on PSP it's quite problematic (or it was some years ago).
I found Grandia very boring and I dropped it after 10 hours or so.
