How would you compare the contents of a cell to the items in a purse?

Because some of the central aspects of a cell's nature are that it's alive, consumes food, produces waste, and responds to its environment, this isn't the best analogy. A purse is just a container, so we end up missing most of the "active" elements of comparison because they simply don't exist in a purse.

The outside of the purse is analogous to the cell membrane, in that it provides structure and support, and establishes the boundaries. The zipper or opening to the purse could be considered analogous to a selective channel protein—only certain things are "allowed" to go into the purse. The purse contents are analogous to organelles in that each one performs a specific function. 

Unfortunately, this is about as detailed as we can get while limiting ourselves to the contents of the purse; we miss out on important elements like the nucleus, which contains the cell's genetic information and guides most of its actions. A purse lacks any analogy to this function unless you start to take its owner into consideration, but at that point you're just comparing the cell to a human and the way a human uses tools.

A better analogy for the cell would be a factory, assembly line, farm, or bakery. These comparisons are more accurate because they focus on production and response, as the cell does, and they are active under their own direction.