Standard white granulated cane sugar is actually the ideal and authentic choice for a classic caipirinha, so there is no need to spend extra money on specialty raw sugars like turbinado or demerara.
In Brazil, caipirinhas are traditionally made using plain refined white sugar. The trend of using raw demerara or turbinado sugar mostly originated in European and North American cocktail bars. In practice, raw sugars have large, coarse crystals that do not dissolve readily in room-temperature citrus juice and alcohol, which leaves an overly crunchy residue at the bottom of the glass. Furthermore, the rich molasses character of brown sugar can mask the fresh, grassy aroma of the cachaca.
Basic supermarket white granulated sugar provides the perfect balance. Its fine crystal structure acts as a gentle abrasive against the lime peels during muddling to express the flavorful essential citrus oils, yet the grains remain fine enough to dissolve cleanly into the lime juice before you add ice.
For the cleanest dissolution, muddle your sliced limes and granulated sugar thoroughly together first so the acid draws out the liquid and melts the sugar. If you find your supermarket brand has slightly large grains, you can pulse a batch in a standard kitchen blender for five to ten seconds to create fine caster sugar at no additional cost.