Rinse everything thoroughly. Detergent left in clothes can cause chemical changes in the fabric. Wash everything in soft water. Hard water can cause yellowing and rust spots. Never put clothes in plastic.
Moth balls can stick to plastic and damage fabric.
Plastic is airtight and clothes need to breathe. So you're better off using fabric. Old sheets and pillow cases are perfect for storing clothes. Just cut a hole at the top of a pillow case and slip it over a hangar, or use a stapler to create storage bags from sheets. Use moth balls only in closed, vented containers , like a coffee can punched full of holes.