Lots of people report good success using the IKEA Bonde bookshelf units. These are 15" deep and each shelf is 14" wide so shelf-sagging under the weight of records is not a problem. Also, the width provides appropriately spaced vertical support for your records (a highly recommended design feature for record shelving no matter what you do). They come in heights of 58" (four shelves) and 86" (five shelves)
You can see a picture of a four shelf Bonde unit in use on Slipknot1's system page.

I'm using something very similar for storage of several thousand LPs here.
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You can see a picture of a four shelf Bonde unit in use on Slipknot1's system page.

I'm using something very similar for storage of several thousand LPs here.
.