The fabrics would look nice in a large shadowbox frame.

I have many collections and display them in varying ways.

I've hung plates on walls in groupings or in a row above my kitchen cabinets.

Tea pots can be displayed nicely in a china cabinet.

I sometimes use vintage lace runners on furniture under vignettes.

Here's a pic of a wall cabinet my DH made with an old picture frame which I've used to display vintage bone china teacups here. I've also used it at other times to display a collection of small pieces of pottery or my collection of vintage glass fishing floats, shells, and other natural items.

The link below is to Pinterest which is a good source for ideas.

Here is a link that might be useful: displaying collections

I have been collecting tea cups since Japan was occupied, and I have a narrow shelf, about 6-8 inches around the entire perimeter of my breakfast room and kitchen to the point where it intersects with the cabinets. My mother was keen on knitting, crocheting, tatting, applique and embroider, so I have a lot of "doily" cloths which I can display on tables, on the shelving, etc. I have cabinets with glass/chicken wire doors where I put cloths on the shelving and let it lap over the edge and display teapots there as well as special glassware, depression glass, etc. I take this in and out, and display my blue plate Sunday dinner style for a period of time, moving them back and forth from my house to the storage house so when I tire of one, I have another. If I displayed all I have, I would have to move out and let the hoarder show take over, but I keep what I am not using in storage.

One way to display your table linen is to hang them from a narrow, decorative ladder.

At one time I had my linens displayed on an old drying rack in the utility room, but the cat kept knocking it down, so I put it up. :)

The best thing for your lace collars, IMO, is to have someone frame them...one per frame, then hang them in a grouping on a wall. I bet you could do it yourself.

Patricia43- Are you collecting Japanese lusterware? I collect vases, teapots, cups and sauces and 7 inch plates. I use the dishes for dessert when I have company. My mother received a set when she married in 1939. I always loved it. There was one plate left when I moved out. I took it and I still have it 49 years later. Here is just a bit of my obsession.
Laura