There are lots of other categories that could be used instead of "Simple," "Martial," and "Exotic."
Sort them by shape (Axes, Bows, Hammers, Blades, Polearms...)
Sort them by application (Archery, Fencing, Hunting, Improvised, Jousting, Personal Defense...)
Sort them by combat role (Archer, Cavalry, Infantry, Siege...)
Sort them by damage type (Bludgeoning, Piercing, Slashing)
Sort them by era (Stone Age, Bronze Age, Iron Age, Age of Faerie, Age of Dragons, Age of Magic...)
Sort them by region (African, Asian, European, Polynesian...)
Sort them by training requirement (Basic, Expert, Advanced, Master...)
The trouble is, while each of these methods makes sense in its own way, they don't really work in a universal fantasy game sense. If there was never a Stone Age or a continent called "Asia," for example, you can't really group the equipment by era or region unless you make them extremely campaign-specific and define those regions/eras first.
The method that make the most sense to me is Application. If all of the weapons are sorted by how they are used, it makes it a little more sensible to assign them out to different classes and backgrounds. For example: NPC commoners, Rangers, and characters with the Outlander background might gain proficiency with a couple of weapons from the Hunting list. Fighters, NPC soldiers, and characters with the Noble background might have proficiency with a handful of Jousting or Fencing weapons. Most everyone would be proficient with a Personal weapon like a cane, staff, or dagger. And so on.