Characters have different base stats, but most of your stats are going to be determined by your job/equipment. IIRC Edea is more of a powerful physical character (knight, monk, etc), Agnes is the mage (black/white mage, etc), Ringabel is the fast one (ninja, thief, etc), and Tiz is kind of an all-arounder. Mixing it up and making Agnes a knight or something isn't really a problem though.
Character level is kind of irrelevant. Your job level directly impacts your stats while in that job. So when fighting bosses it's much better to be in jobs you are competent in and not fresher ones you are trying to level up. Additionally, your tactics matter more than level. In the last parts of the game even at max level and max job level, there are still battles where bosses will crush you mercilessly if you aren't well prepared and know what you're doing against them.
JP increases a lot between chapters. So if you get to a point where the next job level seems like it will take eons to grind out (i.e., level 3->4, or 6->7) start working on other jobs and return to it in the next chapter. Plus it will help give you a more diverse set of abilities for each character, which is useful.
Blessed shield from Norende is amazing. Can carry you through the whole game if you work around it.