I use this cheap basket, which hangs down the left-hand side of the rack:
To keep it from jumping off (experience!), I've secured it with a piece of rope at the bottom. After four years and two bikes, it looks ... really beaten up ... but I still love it
My 30-litre backpack or a grocery bag fits nicely. This is also where I keep my U-lock when riding. Since I got the basket, I've hardly used the top of the rack at all.