If you want to get a PSP, more power to you but why for this compilation? Final Fantasy IV is available on multiple platforms already, including the DS through the GBA port and DS remake and the Wii through the Virtual Console. The After Years is already available on Wii.
As for recommendations, honestly it's hard to recommend a good JRPG on the system that doesn't have better versions available elsewhere. Kingdom Hearts: Birth By Sleep is generally considered pretty good, Tactics Ogre: Let's Cling Together is coming soon, there's a supposedly decent port of Valkyrie Profile, if you haven't played Valkyria Chronicles on PS3 you have Valkyria Chronicles 3 to look forward to (I've heard that #2 is pretty terrible), and The Third Birthday (Parasite Eve 3) is coming soon as well. There's also yet another version of Persona 3 on the PSP, though it's hard to recommend when Persona 3 FES was fine just as it was on PS2. Shin Megami Tensei Persona is something of an acquired taste, but it has had good reviews.