Trim the stems of the arugula. Rinse the arugula and dry thoroughly. Keep chilled until ready to assemble the salad. Combine the vinegar, salt, and pepper. Gradually whisk in the oil. Adjust the seasoning with additional salt and pepper if necessary.
For each portion, toss arugula with ½ ounce dressing. Lift the arugula from the bowl, allowing the dressing to drain back into the bowl. Arrange on a chilled salad plate. Add the watermelon to the bowl and toss or roll until coated with the remaining dressing. Place the watermelon on top of the arugula. Garnish with the red onion and ½ teaspoon pine nuts, if desired. Salt, to taste. Top with a few turns of freshly ground pepper.
*For a Mediterranean touch, add sliced garden tomatoes and cubed feta