It's not possible to display every fabric, so don't stress yourself out about trying to accomplish that. You can help people if they ask for a specific colour.
When I've seen sellers who make fabric items for babies, they often place them in baskets, or vintage suitcases so that people can look through them without making a mess all over the table. Tying the cloths together with ribbon to keep them neat is a good idea.
The boppy covers could be clipped with clothes pins to hang from strings or metal grids. Some people use room dividers or quilt stands, laundry dryers.
One display item that might be of interest to you is tiered baskets, usually 3 baskets all set on a long pole. I've seen tabletop ones, and those that are tall and stand on their own.
Also I like the idea of using vintage doll cribs and cradles to hold the toys or baby items. You can paint them white or a bright colour.