I don't know that rulers being stored flat is a particular necessity...look at all the ruler stands out there! As to mats, yes that is certainly the preferred method. That said, I have mine on edge but having the somewhat sandwiched between a piece of furniture and some containers. Keeps them from wobbling too much and I don't seem to have an issue with warping. I have my main mat on my cutting table all the time but I have other, less frequently used mats, that I store for long periods on end. Even my large, main mat will go on end in the same spot when I am sandwiching quilts and no issues.