I have had to organize more than one storage facilities, usually for smaller items like repair parts. The very first thing that I realized in some of the facilities was that; if you can't find it then you just don't have it. Some of these facilities were so disorganized that it was literally faster and cheaper to just buy new parts instead of finding the ones we already had.
The next thing was that I had to deal with a range of sizes and quantities. The parts that I worked with ranged from small fractions of an inch up to several feet in size. And, of course the weights also varied. This translates upward to your situation where you have items from 6" x 6' up to 4' x 20'. And the weights are also all over the map, but most of them probably require some kind of handling equipment. There are two points here: first, it is not economical to use the same sized storage location for all of them. Smaller ones should get smaller bins and larger ones will require larger bins. However, using just a limited number of standard sized bins is the way to go: 20 foot bins, 12 foot bins, 4 foot bins or some such. You may want different widths as well as lengths. The item goes into the smallest bin that it will fit in. But you don't want too many different bin sizes as that just becomes confusing.
The second point is that, unlike my situations, you will need to consider just how the handling equipment that you have operates and just how stiff or flexible these strips are. Can you shove them into horizontal bins? This would probably produce the most compact storage. But that may be difficult with such heavy items and the isles would/may need to be as wide as the strips are long, well actually just a bit wider. Can you put them on shelves with a fork lift? This would take more floor space, but would be a lot easier to store and fetch them. Again, the isles may have to be quite wide. And shelves do not have to be full shelves; well spaced brackets would work and would allow the forks of a fork lift or other chains or belts to be wrapped around them. If the strips are very flexible, such brackets may have to be spaced fairly close to each other; perhaps 12" or even less. Can you store them vertically in tall bins using some type of crane? If they go in edgewise, this could be more compact than shelves but more floor space may be needed for the handling equipment. If they are very flexible, perhaps they can be hung from hooks, that may be an ideal storage method.
A gantry crane may be the best way to handle them in any of these cases.
I set up a vertical storage system for wood panels that were 4' wide, 12' or more long, and a few inches thick by using vertical pipes that were fastened to the floor and to a roof truss above. I would not put all the weight you will have on a roof truss so you might have to use something more solid than that, perhaps some structural type steel and add some horizontals to separate the bins better for the narrow ones. But these panels were stiff enough to stand up.
Safety is a consideration here also. You don't want any danger of them falling on workers.
The first thing I always did was to devise a locator system. The bins should be numbered in a logical manner so someone can go directly to the correct bin once the locator number is known. You need to decide how many sizes you will need and how many of each size. Each bin has a location number so the items do not need to be in any particular order. A computer will keep track of what is where: you want item # BJ9376 and the computer tells you it is in bin # L235.
Oh, and the most basic rule: ONLY ONE ITEM, BY STOCK NUMBER PER BIN. Yes, this may waste a little space. But it prevents a LOT of confusion. And you did say the present situation is a mess.
Another thought is not to be too stingy on the number of bins. Today you need 200 so build at least 400. Or at least, have that number in mind for future expansion.
As to how to build the bins, I would use things like structural steel: H and/or I beams and heavy duty angle. I would NOT weld them as that makes it very hard to resize the bins if you have more items of a given size than planned. Bolt them together and use a system that allows for the various sizes to be combined in various ways. For instance, if you start with bins that are 20' long/deep, then your next sizes may be 12' and 8' which add up to 20'. So the units will be the same depth and can be located side by side.
One possible exception to the "don't weld" injunction would be for a horizontal base on a vertical post. These could be welded as disassembly may not be a consideration in ordinary use. Of course, diagonal braces would be needed in either case.
The above is a bit disconnected as I lack many of the details that I would base something like this on. The available handling equipment and the available space would be the biggest two such items.
There are probably ready made systems that would be an excellent way to do this. I have no doubt that they would be expensive.