I have a decent library of parts kits and I've had to face the same issue....how to store everything, what to keep together, and how do I find what I need in the pile?
When I break down a kit, the first step is to inspect the stocks and put them together loosely with the stock screw and a tag identifying the frame size. If the stocks are numbered, the serial number goes on the tag. That's more for identifying the age of the stocks than anything else. Stocks numbered to guns that I own go into the back of the safe when they're not on the gun they came with.
Next, the small "generic" pieces go into a divider box. These are the strain screws, bolt/bolt spring/bolt plunger, sideplate screws, orphan stock screws, stock pins, cylinder stop springs, thumbpieces and nuts, hammer blocks, rebound springs, rear sight screws, barrel pins, rear sight assemblies, hammer springs, and orphan yokes, hammers, triggers, hands, cylinder stops, and rebound slides.
The major parts are made up into packages. The barrel goes into a small snack bag by itself. The cylinder, yoke, and ejector assembly go into another small snack bag. The trigger, hammer, hand, cylinder stop, and rebound slide go into a third small snack bag. These 3 sub-groups are then put into a sandwich bag that is numbered and has a short description written on it with a sharpie.
Sideplates are stored in a flat box with alternating layers of bubble wrap keeping them from scratching each other.
The bags are stored in a locked cabinet, the bin box is under my workbench, and the sideplate box is on the shelf with the stocks.
The bag number and a description of the contents are kept on a notepad on the workbench in my own personal shorthand. For example, "53 - 4" M15 .38 TB NR full N" means that bag #53 contains a 4 inch Model 15 in .38 special with a tapered barrel, non-recessed cylinder, it's a full kit that isn't missing any pieces, and it has a nickel finish. When I use a kit for a project, I use the very high tech method of drawing a line through it on the list.

If I don't use all the pieces, the orphans go into the small parts organizer box.