What pieces of eqipment are safe to sell?

Just like Final Fantasy 7, the sell screen for Final Fantasy 6 is perhaps enragingly... lacking.

^{There's a pane for character portraits on both the buy and the sell screen, but the sell screen's is inexplicably empty. Sigh.}

Given that you can unequip party members in this game through the convenient "Remove all" button on the Equip screen, the only reason for holding onto old stuff is if you somehow like to scroll through pages of junk.

The selling situation on FF6 is especially difficult because most of the items are only available for a subset of characters. Moreover, for most of the game most of your party will be unequipped, so even if the sell screen had character portaits, it'd be kinda useless.

Finally, for most of the game you'll only need equipment for 4 people — until you hit the Narshe battle and the end game. That said, the Narshe battle is kind of early on, whereas by the end game you should have enough gil to buy and obtain top-notch equipment for your party anyway.

So... what items can be sold safely in Final Fantasy 6?