I use the zip lock bags a lot, all sizes, and the idea of using a paper plate to organize within the bag is a great idea. Thanks to you all who recommend the dollar-type stores for those bags which don't have to be the expensive freezer ones.
I've also used the large size plastic container that pre-washed salad comes in, nice and deep and easily stored. ..not for long-term storage of fabric, but to help organize "stuff."