In terms of ease of identifying known parts, folders by company followed by part numbers is probably the best solution. In terms of ease of design with unknown parts, sorting by gear DP, then listing the tooth count (easy to sort by), manufacturer, bore, and I guess overall width (is every AM gear .4 or .6? every vex gear is .5) would probably be the best way to do it. So there's some conflict here.
Personally I don't really have brand loyalty when it comes to gears, so I'd want a system that just lists all of my options in the same place. I'd rather not have to dig through a series of folders like AndyMark -> 20 DP -> .375 Hex -> 14T just to find a pinion. Folders just by gear DP narrow down the options without hiding anything potentially viable.
So I guess my ideal system would be folders for gear type (20 DP, 32 DP, Specialty [worm, bevel]) and then a big custom identifying name. Part numbers would be nice if I could learn anything about the gear at all from them, but in this context it's not that helpful for anything but the end of the process when I want to buy stuff.
So, for example, in the 20 DP folder:
21T-AM-375H-588 would correspond to
this gear. The gear has 21 teeth, a 3/8 hex bore, and .588 overall thickness.
48T-Vex-500HVK-500 would correspond to Vex
PN 217-3218. This is a 48T gear with 1/2 hex bore, VersaKeys, and .500 overall width.
This probably could be improved on, but this is what I would find most convenient for myself. Others' mileages may vary.