1. Prepare the sushi rice according to package directions, then fold in the rice vinegar and let it cool completely to room temperature.
2. Slice the raw sushi-grade salmon into long, thin strips and slice the cooked shrimp in half lengthwise.
3. Peel and julienne the cucumber into thin matchsticks and slice the avocado into thin wedges.
4. Place one nori sheet on a bamboo rolling mat and spread half of the rice evenly over the bottom two-thirds of the sheet.
5. Arrange half of the salmon, shrimp, cucumber, and avocado in a horizontal line across the center of the rice.
6. Lift the edge of the mat and roll the nori tightly over the filling, using a drop of water to seal the outer edge.
7. Repeat the process with the second nori sheet and remaining ingredients, then use a sharp, wet knife to slice each roll into eight even pieces.
8. Serve the fresh sushi rolls immediately with tamari, wasabi paste, and pickled ginger on the side.