How does this question differ from What items are worth picking up? That question is more about what items are worth keeping between home-runs, so to speak. My question is more about longer term storage and selling.
In Path of Exile, there's no gold (piece) economy. It is based on currency items which each have their own use and their prices are relative. It's a barter economy. The other integral half of the economy is combat items: weapons, armour, jewelry, maps, and skill gems.
Among what determines a weapon's or armour's worth are: sockets, links, item-level, and the mods that are on it. I want to focus on the mods. There are two types of mods, implicit and affixes. Implicit mods always come with a certain weapon type. The more important type of mod are affixes.
Mundane (non-magic) items are items without affixes. Affixes are split into two categories: prefixes or suffixes. A magic (indigo) item can have up to one prefix and suffix. More than that and it becomes a rare (yellow) item.
Now, you may say that what determines an item's worth is the mods that you're looking for, which can vary greatly. I believe that it doesn't vary greatly. While the mods that are desired differ based on build, there are certain sets of mods that are desired on each individual item (weapon, jewelry, and armour pieces (chest, helmet, gloves, and boots)). The most-easily-notable universally-desired sets are Increased Item Rarity + Increased Item Quantity (A.K.A. "Magic Find") and elemental resistances + increased armour/evasion/energy shield. I could name maybe a few more, but I'll leave the rest to the answerer.
What determines whether an item is worth selling on the market, vending to an NPC, or auctioning (particularly, in terms of mods/affixes)?