Here is a recent question regarding storing linens.
I had exactly this problem which was exacerbated by the fact that when a set of napkins were sold, I not only needed a way to find them easily but also to be able to pull them out of a box or a stack without wrinkling them or wrinkling the other items in the stack. My solution is to use cardboard panes, one for each set of napkins. But first I cover the cardboard in white tissue paper to keep the cardboard from touching the fabric.
I tie ribbons around each set of napkins in order to keep them tidy and together. Lastly, I attach a tag that tells me what they are. I try to place each tag in a different place on the cardboard so that I can see each one at a glance and I keep them facing front.
Even if the set that I need is on the bottom, I can easily lift the entire pile, extract them and replace the rest because they are supported by the cardboard.

The tag identifies a set of placemats in storage. The tags for the sets beneath this one are staggered along the front edge.
Although I devised this system for myself through necessity, it doesn’t surprise me that other people have come up with similar systems. For instance, I recently acquired linens from an estate of persons of great wealth which meant that they had multitudes of everything. I was amused to see that all their linens had been sent out for laundering and the laundry had packaged the linens to perfection BUT had laid them directly on flimsy, inexpensive cardboard and then wrapped them in cellophane!
Here is another close up.

They looked lovely, all bundled up! But, when removed from the packaging, they were actually quite stained, much of it coming from being stored next to substances that off-gas chemicals.
They were placed so carefully, alternating tops and toes, with only four to each package. I suspect that nobody could predict that they would be put away and not opened again for decades.
It does take decades and decades of poor storage to ruin things, though. I have seen linens that were rolled in newsprint or on cardboard paper towel cores that were exposed to those particularly acidic papers for 40 or more years and, besides needing to be laundered, fared pretty well. The worst thing you can expose your linens to is humidity and damp!
Go organize your linens! But enjoy doing it.