My mother always hangs laundry outside to dry on the line, so our laundry baskets do a lot of work. We also use them to haul things in and out of the house. Wicker laundry baskets are becoming difficult for us to find, and the handles of cheap, plastic baskets break far more quickly than is reasonable.
In our experience, nothing beats a bushel basket made of poplar wood for a sturdy hamper. The same type as many people use in the garden, these baskets are sturdy and readily available, as are the vinyl liners, which we purchase from the Lehman’s catalog. You could also make your own basket liner out of oilcloth or a plastic tablecloth. Happy washday!