You may want to wait and see how things go before investing in a set system (granted the storage drawers aren't too pricey).
The reason I suggest this is that the proportions aren't what you may think. For example, in a single day, an adult rabbit will eat roughly a bucket full of hay but just a couple tablespoons of pellet feed. That would leave you food drawer practically empty.
Treats should be offered even less and fresh (or dried) fruit is the best treat (no store-bought packaged "treats" because most are terrible for rabbits). Fresh fruit won't be stored, then, in the drawer.
Your rabbit will also be getting accustomed to daily greens. Those too, would be in the 'fridge.
Toys may be ignored by some rabbits. Of all the rabbits I've had, only 1 or 2 actually played with toys. But most liked to chew up large cardboard boxes or TP tubes.
To answer your question of how
I store things:
I keep a kitchen trash can full of
hay in my laundry room (a few steps away from bunny's cage).
Pellet food is kept in the jar on top of the cage (along with a pitcher of water). You can see this in the photo below.
Greens or fruit are in the fridge. But I do keep a small container of dried banana next to our couch. Bunny gets a little in the evening when he tends to hop out to the couch area.
I should also add, just for space comparison, that the kitchen trash can full of hay has to be refilled more often than that little jar of pellet feed on top of the cage.
And just for fun... here is that treat jar - empty - but he's trying to get more!
