I'm a paper snob and know most of my lines really well. So I sort by company BG, American Craft what ever and then by line. I can tell you within one or tow minutes what line something is scrapped with. So I usually have a pretty good idea of what I have at any one time. I have probably close to 20 inches of patterned paper but can tell you what I'm hunting for So I guess what I'm trying to say is if you know your lines really well sort by lines.
this is me. I sort everything by company and paper lines in 2 gallon ziplocks bags.
All of my pads are standing like books on a shelf. I have two of these Cropper Hopper for single sheet paper and kits.
I do the same - pads on the shelf, loose pattern paper in the cropper hopper by color, separate storage for solids, small basket for 6*6 and smaller scraps. I also like to flip the papers so I can see both the front and back side, if there are two sides and two papers.
I like to keep the collections together, so if I pick up loose papers with the same line or collection, I pack it in a ziplock and store on the shelf with the other collections. once it's down to a couple papers, it goes into the hopper.
I also recently separated loose striped papers into a separate unit - super helpful, since striped papers aren't usually of a particular color, it's hard to sort them. now, whenever I need some stripes, I flip through that section and find the color combo that fits.
I have some cues with slots. I do what many of the ladies here said: cardstock by color, and everything else by brand or theme.
Also, I generally buy special papers, one or 2 collections for vacation albums, and I keep them separate until the vacation album is done.
In addition, I go through my papers every couple of years and put things that don't appeal to me in a box in the attic. That gets them out of my way. I can always go get them if I suddenly remember that I want one, or I can go there if I have a donation opportunity.
There are apps for your phone that allow you scan your products and keep a digital list of what you have. I know what you're talking about. I have a store room that is packed to the max with with seasonal decorations, tools, clothes and other household supplies. I recently went through it. It took me a couple of WEEKS. I took photos as I organized each area. Now I'm going to create a "book" that will be my map to find everything in that room when I need it...lol Maybe you can do the same thing with your paper :-D