Add potatoes to a pan and cover with water. Add 1 Tbsp. salt. Bring to a boil over medium-high heat. Simmer until potatoes are tender, about 10 minutes. Drain and place in bowl.
Whisk mayonnaise, sugar, vinegar, mustard, 1 1/2 teaspoons salt, and 1/2 teaspoon pepper.
Add dressing to the potatoes and stir to combine. Stir in onion, celery, and chopped eggs. Garnish with paprika if desired.