Back in college we had a rack like Footer posted and it was oriented like you're thinking, it was tough to get certain sheets out sometimes (if we had something stacked under a different type of sheeting for some reason). Sliding them in and the long way wasn't too big of a deal. Depending on how high you go with that though you may want to think twice about the
flat storage above, wouldn't want it high enough that you need a ladder to get flats out, I'd much rather be standing on the floor when I do that, just a height thought.