To be completely concise...
FFI: Fight and get exp. Stats based on class. All items and spells are purchased. No AP.
FFIIj: Fight to increase stats. Most items and spells purchased, except pre-determined characters. No AP.
FFIIIj: Fight and get exp. Most items and spells are purchased. Stats based on job class system. AP used for job-change. Invisible AP for job mastery, based on battles fought, survived, and class. Everyone KNOWS this is the best.
FFIV: Fight and get exp. Pre-determined levels for stats and spells.
FFV: Fight and get exp. Stats based on job class system. AP used for Job mastery.
FFVI: Fight and get exp. Magic pre-determined for levels with Terra and Celes. All other magic learned by Esper. AP used for Esper/Magic learnage.
FFVII: Fight and get exp. Magic usage based on Materia, all stats are static per level except HP growth. AP used for Materia.
FFVIII: Fight and get exp. Junction/Draw system for magic.
FFIX: Fight and get exp. Stats are static over all levels. AP used for support and other magic abilities.
FFX: Fight and get AP. Stats are static until Sphere level 45/extra spheres. Magic based on level, non-static. No EXP.
FFXI: I assume... fight and get exp. AP used for learning stuff.