I've got a Wald 585 basket on my commuter, held to the side of the rack by hose clamps. Some innertube rubber between the basket and each clamp reduces rattling and loosening. It's lasted 20 years so far. Most bikes can accommodate this basket, but you may have to set it back in order to avoid heel strike, depending on your bike geometry.
And they're cheap, one of the best bargains in all of cycling.
https://www.amazon.com/Wald-Rear-Bic.../dp/B001AYKN84