I went with a system my buddy came up with. He used to move around a lot and needed a way to easily move them without packing and unpacking them. They are essentially boxes that can be stacked in any arrangement to accommodate any area.
Here is a pic of a box for my 7 inch vinyl:
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The tops and back are three pieces of 8 inch by 24 inch long. The dividers are 7 inch wide by 8 inch tall, all 1/2 inch thick. Because the top and bottom is 8 inches wide the vinyl does not hang out past the edge.
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If you pick up the box by the lip on the top (or bottom), you can turn it on it's back and stack them for transport if necessary without crushing the contents.
I made boxes for my 12 inchers first so I was sort of developing the sizes needed. The tops and bottoms are 14 inch wide by 23 inch long, 3/4 inch thick. The backs are 15 inch tall by 21 1/4 long so they overlap the top and bottom pieces for strength, 1/2 inch thick. The dividers are 14 inch by 14 inch, 1/2 inch thick. The joints where the sides attach to the top were rabbited, glued and screwed. (my pal glued and clamped only for appearance) Glued and clamped only is probably plenty strong. I did the rabbit joints myself on a table saw after the pieces were cut-to-size. They may not be necessary but probably add a lot of strength.
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I made a bunch of boxes for my CD's as well.
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Advantages of this system are you can stack them any way you like and pile lots of garbage on top or place equipment on top.
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The disadvantages are the higher you go, the less stable the arrangement becomes. Not so much a problem with wider LP boxes but my CD bowes are actually anchored at various points with small hooks and stainless tie wire. When I stacked them I offset the boxes to add a bit of stability.
They can be assembled easily with simple hand tools. The cost may seem a bit high but once they're made they're done forever.
Also, I was involved in the plywood and furniture industry for quite a while so I had some connections. This is important; I had the wood cut for me by a professional. Small time furniture company but he had some righteously top-of-the-line computerized panel saws. The cuts he made were razor sharp and the pieces were absolutely square. Also, because he cuts truckloads of wood he had plenty of inventory. The local HOME DEPOT was charging $26 for a 1/2"x4'x8' sheet of Mahogany. The shop where I went charged me about $18 per sheet, cut to size. This particular shop did not advertise, of course, because the guy was a wholesale-only cutter/manufacturer.
My point is with a little bit of leg work and careful planning (try not to incorporate too many different sizes for each set of boxes) these can be made reasonably cheaply and the results are good. I even went so far as to buy the clear finish in a can and apply it with a brush. Much cheaper than spray cans. I then lightly hit them with 300 grit sandpaper, wiped with a damp cloth, good to go.
All of my best vinyl is packed in Japanese resealable sleeves. Everything else in poly sleeves. Slide them in and out, no shelf wear.