Welcome to the club Xenmasta
Jeanne D'Arc - is my favorite game on the PSP. A very unique take on Joan of Arc as a tactical game.
Followed closely by:
Persona 3 Portable. Play as a female with all new Social Links.
Valkyria Chronicles 2 - Its VC2! Need I say more?
Final Fantasy Tactics - Same old game with some added cutscenes.
Tactics Ogre: LUCT Branching story in a tactical game. Changes a good bit of everything depending on what you do.
Persona 1. Branching story. Can have many different characters in your party based on your decisions.
You and I have very similar tastes and I have no doubt you will enjoy the hell out of the above.