I overcast the raw edges before washing - even the fat quarters.
I use either a narrow longish zig-zag - or the longest narrowest serger stitch to overcast the edges.
About the most fabric I lose is about an 1/8 of an inch on each edge.
I just toss the pieces in the dryer. No tangles. Really long pieces tend to wad up or ball up and I check every so often and unwad it and then put the fabric back in the dryer. The fabric is more apt to wrinkle if the dryer is overloaded.
Narrow pieces - 1/4 yard or less - seem prone to tangling - it might be good to put them in a case before putting them in the dryer.
Tiny pieces I just hand wash and air dry - I don't (usually) overcast them - and put them either on a towel or on those meshy sweater drying things. They could be put in a bag and spun dry and then dried in the dryer. Might have some fraying, tho.