Put the potatoes in a large pot and cover with cold water by 1 inch. Add 1 tablespoon of salt. Bring to a boil, then reduce the heat and simmer for 10–12 minutes, until a fork slides in easily.
Drain well. Spread the potatoes in a large bowl, sprinkle with 1 tablespoon of vinegar and let them cool for 20 minutes.
In a small bowl, stir together the mayonnaise, mustard, relish, 1 tablespoon of vinegar, ¾ teaspoon of salt and the pepper.
Add the eggs, celery and onion to the potatoes. Pour the dressing over the top and fold gently until everything is coated.
Cover and refrigerate for at least 2 hours. Taste, adjust the salt and sprinkle with paprika before serving.