What pieces of equipment are safe to sell?

Solution 1:

I've collected information about all pieces of armor in the game and fed it to a little bit of Python 3 which gives me this chart, where the arrows mean " → is better in every possible way than →". This pushes better items at the top and worse items at the bottom.

                   (better armor)

                                                  (worse armor)

Click for bigger, searchable version

^{Footnotes: (1) Tifa, Aeris, and Yuffie only (2) Cloud, Barret, Red XIII, Cait Sith, Vincent, and Cid only.}

How to read this chart:

• If X → Y, it means that X is better in every possible way than Y.
• If X → Y → Z, it means that:
  • X is better in every possible way than Y
  • Y is better in every possible way than Z and
  • X is also better in every possible way than Z (this is necessary to make the chart readable, or you get this).
• If an item is not in the diagram at all, then it's neither better or worse than any other item, so... just don't sell it.
• In all versions of Final Fantasy 7 prior to the 2012 PC re-releases, the magic defense stat on all armor is purely cosmetic: it only appears to have an effect on the equip screen. If you are playing the Steam or Square Enix store versions of FF7, ignore the grey dashed arrows.

In other words, if you can make a path following the arrows from an armor to another, then that other armor is worse than the first in every possible way. So, for example, the Dragon Armlet and the Gold Armlet are both better than the Shinra Beta, but the Dragon Armlet has elemental damage halving whereas the Gold Armlet has better stats in general, so neither is perfectly better than the other. When you acquire the Diamond Bangle, therefore, you can safely sell the Silver Armlet but not the Dragon Armlet.

What about weapons? The results are somewhat less interesting because all weapons can only be used by one character, and some characters have different guns dealing damage of different elements, so this splits the diagram quite considerably. Here they are, nonetheless, this time from left (best) to right (worst):

(better weapons)                     (worse weapons)

Click for bigger, searchable version

Solution 2:

I tend to follow a rather conservative rule of "if I bought it at a store, and that item is at least 2 store-grade-items out of date" then I consider it safe to sell. Additionally, I don't tend to sell unless I need cash for something.

So for instance you go to NPCville and you buy a shiny Bronze Sword, and then you visit NPCtowne and they're selling a Steel Sword. I probably wouldn't even buy the Steel Sword in this case, and I'd probably not sell the Bronze Sword if I did. But once I reach NPCtopia, and they're selling a Magic Sworde, but I can't afford it, I'll sell off my Bronze Swords to pay for it.

In FF7 in particular, I'd hang on to things that have a lot of Materia Slots or high Materia growth if you plan to grind some of the more difficult Materia up to their "master" states. Even if the weapon sucks, you're still getting bonus AP out of them. Everything else I'd sell as per my plan above.