Most of the vinyl storage products I see for sale, and most of the ones people have built store the vinyl horizontally, or mostly horizontally. But I could have sworn I read somewhere that vinyl is supposed to be stored vertically. I'm trying to clean up my shop, and storing my vinyl is a concern. I want it out of the way, but before I buy or build something to store my rolls, I want to make sure I'm storing it correctly.

You're right - I believe that the reason, though, to not store it horizontally is due to compression/squashing thus making the roll lopsided and not adhering properly.  The horizontal storage units typically support the rolls from within the center of the hard tube the vinyl is wrapped around so it does not compress on the lower side.  Also, if you were just laying the vinyl on its side, there would be a tendency to stack them up like firewood and that would really cause issues.  I'd also warn that storing vertically will sometimes let you get in a sloppy habit of dropping the roll onto the storage unit the last little bit and that will "bung up" the end of the roll also causing issues.  Care in handling is probably the most important order of the day.   

My rolls are taking over my floor. Think I may go ahead and get the wall rack to free up some valuable real estate and lessen the competition between the clutter and myself. I read somewhere that these usually don't come with the hardware for mounting--any suggestions on what to use. It would be disastrous to have it fail because of improper hardware.