Stir the sugar and water together in a large pitcher until the sugar dissolves. Measure out 1 cup. Puree the fruit and the 1 cup sugar water in a blender. Pour the mixture through a fine-mesh strainer back into the pitcher with the sugar water, mashing with a whisk or wooden spoon to eliminate any pulp. Taste and add more sugar, if desired. Serve over ice, with a lemon or lime wedge, if desired.