I keep them in plastic bags sorted by creature type.
I recommend the bestiary boxes and the AP specific one for any AP that you plan to play. You don't need 'all' of them - because they aren't 'every' monster you will always be missing some - having most of the basics (in multiples) helps though :)
I'd recommend reading a few product reviews on Paizo to get ideas on which sets to buy. The Bestiary Box is indispensible as is the NPC Codex Box. The rest depends on your specific needs.
I use cardboard dividers to store my pawns in the Box sets. Each box can hold an additional one or two smaller sets.