For a full experience I recommend, without knowing your economic state, in this priority order:
Core rulebook
bestiary 1
Advanced players guide (mandatory)
ultimate magic
advanced races guide
monster codex (if you run your own campaign)
Ultimate campaign (if you run your own campaign o kingmaker)
other bestiaries
Gamemastery guide
ultimate combat
ultimate equipment
Inner sea world guide, plus path of prestige and inner sea gods (plus incoming inner sea races) for a full golarion experience
Next things are not necessary:
advanced classes guide is not so good
strategy guide for new players
npc codex is just a collection of npcs. Only if you need them
occult adventures if you want the "official" and new psionics or "ultimate psionics" if you want 3.5 ed psionics
mythic adventures if you want something like epics