When creating a granny square bag or purse I would recommend using a smaller size crochet hook or placing a lining within your bag so items are not falling through the holes. The exception would be when you are creating a beach bag so you do not have sand within the lining itself. You can use many different types of granny squares to create a wide range of bags and purses. I recently came across a simple granny square bag with the price tag of almost $3000.00!
Lots of images available for granny square purses!
Here's a few video tutorials for granny square bags to get you started...
Fat Bottom Bag
Easy Crochet Beach or Park Bag Pt1
Easy Crochet Beach or Park Bag Pt2
Can't forget the handles!
Handles for the Fat Bottom Bag
Then the lining and zipper...
Adding Lining and Zippers to Purses and Bags Pt1
Adding Lining and Zippers to Purses and Bags Pt2
Here's a chart demonstrating a few different ways you can put granny squares together to create a bag or purse.