As a Brazilian myself, I prepare Caipirinha in a slightly different way: the ingredients are still the same (although you can substitute the cachaça for dark rum - it will then be called "Caipiríssima"). You should crush the sliced lime (unpeeled, please!) and the sugar in a glass, mix in the cachaça (or rum) and a few ice cubes. As for the comments on using either limes or lemons, I can assure you that what is sold in the US as lime is exactly what Brazilians call "limão Tahiti". So, go with the lime!