I have basket like this (they can be found cheaper): Amazon.com : Basil Cardiff Rear Basket, Black : Bike Baskets : Sports & Outdoors

I use it for groceries and stuff. It fits a smaller backpack easily. It is awesome because you can use the bags you have.

My current bike has a front walk basket. A deeper on that fits a purse easily. They are $20-25 dollars. I love front baskets.