I have my fabric wrapped onto acid-free boards & stored in bookcases out of direct sunlight. I sort them by size (FQ, 1/2 yd, 1 yd, > 1yd) and then by color.
I do keep my FQ in plastic bins, but they get so much usage I don't worry about mildew or bugs.
I do use starch on my fabrics and haven't had issues with bugs, but then I only starch when I press them for a project, not before.