Nice project, and best of all pretty safe.
One particularly photogenic type of battery was known as a “gravity cell,” because gravity is what held it together. Typically used to power telephone and telegraph circuits, it consisted of a solution of blue vitriol (known these days as copper sulfate and sold in garden centers for pond treatment) on the bottom and a layer of zinc sulfate on top, kept separate only by their slightly different densities.
At the top, the electrode gives off zinc ions, while at the bottom, copper sulfate is reduced into copper metal. Together these complementary reactions produce just over one volt; string five batteries in series, and you get enough power to run a flashlight or charge an iPod. Any movement disturbs the delicate layers, ruining the battery, but if you’re careful, you can drop in new crystals of blue vitriol as needed, and the battery will run for years.
Copper sulfate is fun to play with by the way. If it’s heated to drive out moisture and left to cool you get a nice exothermic reaction when you add a drop of water to the pile of powder. Your not going to heat a meal but it does produce a little steam.