Grocery panniers (like
this one ) affixed to a good solid rack work well for me; I find it also helps bike stability if the grocery weight is as
low as possible, as
balanced as possible side-to-side, and if there is also some weight in the front.
With no weight in the front a rear-loaded bike gets wonky steering. You can get detachable front baskets for shopping; I've also just hung plastic shopping bags from my handlebars in a pinch. Even a little weight in the front makes a significant difference in the bike handling.