I use the 2 gallon zip lock bags. I think they come in a box of 4 or 5 for about 4 or 5 dollars, so about $1 each. I can usually fit fabric and pattern for up to a king size top in each one. Throws can go in a gallon zip lock.
I do love the idea of the paper plates as a way to separate the pieces you are working on, but I usually use the 1 gallon bags, a paper clip and a postit note to tell me what the parts are. I do some paper piecing and most of it is Judy Niemeyer. She is the champion of using different bags for different parts of a project.