Dissolving sugar in a beverage
Most cocktails use sugar syrup (e.g. simple syrup with a water to sugar ratio of 1:1 or 1:2) instead of granulated sugar. This eliminates the need to dissolve the grains in - typically cold - liquids.

When you consider powdered (confectioner's) sugar because of the smaller grain size, remember that they will most likely contain anti-caking agents like starch or tricalcium phosphate. I'm not entirely sure how much this would influence the final taste, though.