The big problem with potato salads you buy in stores is they don't cook the potatoes right. Sometimes the potatoes are overdone and mushy but usually they're underdone and crunchy. Crunchy potato salad is no good. Anyway I've got two recipes for potato salad, one from NY Times and one from Serious Eats, but the NY Times one is the one I use; I haven't tried the SE one.
Here's the NY Times Cooking recipe, it is a very traditional and basic recipe, many comments say this is how their mother used to make it. I like it a lot. This is a PDF:
This second recipe is the Serious Eats recipe. As of this writing I haven't tried it yet. The recipe uses 4 lbs of potatoes so it probably makes a big batch, but recipes like potato salad can easily be cut in half. As the Serious Eats article points out, the potatoes in potato salad should never be crunchy or firm, but they also shouldn't be like little cubes of cold mashed potatoes. Their solution was to start cooking them in cold water that you bring to a boil, but based on my experience (like in clam chowder) the real requirement is just keeping a close watch on them to get the right texture.
Ingredients
4 pounds (1.8kg) russet potatoes, peeled and cut into 3/4 inch cubes
Kosher salt
1/4 cup sugar (1 3/4 ounces; 50g), divided
6 tablespoons (90ml) rice wine vinegar, divided
3 ribs celery, finely diced (about 1 cup)
1 medium (8-ounce; 225g) red onion, finely diced (about 1/2 cup)
4 scallions, green parts only, thinly sliced (about 1/2 cup, optional)
1/4 cup fresh parsley leaves, washed and minced (optional)
1/4 cup chopped cornichons (see notes)
2 tablespoons whole grain mustard (more or less to taste)
1 1/4 cups mayonnaise
Fresh ground black pepper
Instructions
1. Add 2 quarts water to a large saucepan. Add potatoes, 2 tablespoons kosher salt, 2 tablespoons sugar, and 2 tablespoons vinegar. Bring to a boil over high heat. Reduce to simmer, and cook, stirring occasionally, until potatoes are tender, about 10 minutes. Drain potatoes and transfer to rimmed baking sheet. Spread into even layer, then sprinkle with 2 tablespoons vinegar. Allow to cool to room temperature, about 30 minutes.
2. In a large bowl, combine remaining sugar, remaining vinegar, celery, onion, scallion (if using), parsley (if using), pickles, mustard, and mayonnaise. Stir with rubber spatula to combine. Fold in potatoes. Season to taste with salt and pepper. Cover and rest in fridge for at least 1 hour and up to 3 days before serving.