I prefer a rigid basket. I've had a Wald 585 for almost 20 years, and a couple more Wald baskets that my dad had for years before giving to me. I attach them to my rack with stainless hose clamps, and some innertube rubber to keep them from rattling loose. One is on my commuter, and another on my winter bike.

Big enough to hold a regular shopping bag, or a backpack. I don't need to open or close anything, but just throw stuff in and go.