Add potatoes to a large pot, add a teaspoon of salt, and cover by about three inches with cold water. Bring to a boil, turn down to a simmer. Cook until potatoes are tender about 20 to 25 minutes.
Add eggs during the last ten minutes of the cooking process; remove them and plunge into ice water when finished. Watch the eggs, just in case the ten minutes pass before the potatoes are tender.
Drain potatoes and spread on a large sheet tray to cool. When cool enough to handle, but still warm, dice into bite-sized pieces, sprinkle with vinegar, then salt and pepper. Place in refrigerator to continue to cool.
In the meantime, make the dressing. Combine the mayonnaise, sweet pickle relish or sugar, dry mustard powder, ballpark mustard, celery seed, and salt and pepper.
Peel and chop the hard-boiled egg into bite-sized pieces.
Once the potatoes are cool, add them to a large bowl. Add the hard-boiled eggs, celery, onion, and dressing. Using a large spoon or spatula, mix to combine. The salad is best if some of the egg yolks deteriorate and get mixed into the dressing.
If the salad seems dry, add in water by the tablespoon and mix after each. Do not add too much water; add just enough to make it creamy! Chill, and once cold, taste and adjust flavorings, adding more mustard, relish, salt, pepper, etc., if needed.
Garnish as desired.