I've showed it in other similar threads, but why not again?
I've found that this might not be the most artistic, but it sure is functional and very easy to build early-game.
Unless you are running a multiplayer server and you are mass-hoarding items, the setup you see here is overkill for anything you'd need to store in an average single-player playthrough and I'll go over what each chest is, and what it contains:
1). The wood chest sitting off to the left: That would eventually become where Seeds are stored (most likely, rows of planters would be set up near that woman statue that you see).
2). The Ivy & Glass Chests you see below it. Glass Chest is for Potions, Ivy Chest is for ingredients to make alchemy stuff. In this screenshot, I don't yet have an Alchemy Table (it goes right next to the glass chest) and that little nook next to the ivy chest gets filled with 2 tiles of water for making bottled water.
3). The row of wooden chests below the crafting machines. The first four are, in this order:
a). Easymode Ore & Bars
b). Easymode Materials (that are NOT ore, bars, or gems)
c). Hardmode Ore & Bars
d). Hardmode Materials (other materials usually only gotten in hardmode)
The 5th chest tends to be for fishing stuff, the 6th for mechanics, the 7th for dungeon related junk (hardmode, that is), etc.
4). The Gold Chests: The first chest in the bottom row is for accessories that will be combined later. The rest of the chests are for storing weapons, armor, and accessories (I only keep one of each unless it can be combined or used in a crafting recipe). With the number of chests you see here (and also that can be placed until the end of the row), I have never, ever run out of room.
5). (Not Pictured): A Row of Ice Chests: I will normally place a row of blue chests on the very bottom underneath the gold chests. These contain all vanity items and mounts, and I usually devote 1 of these chests for statues (usually the first on the left).
Now with those wooden chests, I will normally use Marble for the Hardmode stuff (I'll swap em out later, I'll use wooden chests as placeholders), and I'll usually use a water chest for fishing so you can more easily tell what chests are for what without having to mouse over them.
The beauty of this system is that:
1). The area with the chests can be run through without having to stop, jump, or otherwise navigate terrain.
2). The Crafting Material Chests, Potions, and Ingredients can all be reached by Quick Stack.
3). The Main Crafting Machines are close enough to the Main 4 Materials Chests that you can craft just by opening a chest.
4). Everything else is easily accessible rather quickly (in later playthroughs, I made the dryad's room accessible from the gold chest room).
Like I said, not pretty but very functional. It wouldn't be good enough for the hoarders, but yet it is plenty for the person who only keeps a reasonable amount of materials.