making quilts since 1976...i have never stitched edges of fabric before washing it. i throw it in the wash i throw it in the dryer...if it is small pieces (smaller than a fat quarter) i put it into a mesh laundry bag, other than that i just wash it. and yes, some does fray, and some does shrink...that's one of the reasons i wash it in the first place. when it comes out of the dryer i set up an ironing board and a small cutting mat side by side, i trim/clean up edges and press it all...sometimes i make an afternoon of it and just really enjoy touching it, admiring it, dreaming of the wonderful things it may someday become.
just get it washed and dried before you have real problems (like mildew) and maybe you could use rubbermaid totes in your cabnets to protect your fabrics from moisture?