Rinse and drain rice. Cook according to package directions. Meanwhile, combine vinegar, sugar, and salt in a small bowl. Spread rice in bottom of a large, shallow bowl. Sprinkle vinegar mixture over warm cooked rice, stirring gently until well blended.
Cut tuna into 1/4- x 1/4- x 7-inch pieces (about the width of your pinkie). Chopping chunky fillings such as shrimp may make rolling easier. Set aside.
Cut nori sheets to make 4 (5- x 7-inch) rectangles. Place nori on bamboo sushi mat. Spread 1/2 cup rice mixture on one nori sheet, leaving a 3/4-inch strip of nori on the long side uncovered.
Place tuna and desired fillings along center of rice. Holding fillings in place in the center of the rice, and roll up bamboo mat, pressing gently, until rice and nori encircle the fillings. Stop rolling at the point of the exposed strip of nori. Lift bamboo mat up slightly, and turn nori roll over a little so the uncovered strip of nori can seal to the roll. Press mat to seal roll.
Cut roll in half with a sharp knife, then cut each half twice to make 6 equal-size pieces. Repeat with remaining rice, tuna, nori, and fillings. Serve with soy sauce, wasabi, and ginger, if desired.