This is an old-school potato salad: creamy with mayo. I am also dying to try the "french" type version that uses an oil based vinaigrette instead, like this recipe from La Tartine Gourmand, which features radishes, cucumbers, and watercress in a lemon/dijon/tahini dressing.
Cook potatoes (any variety seems to work), either by boiling or my favorite, pressure cooking. This website has a list of pressure cooker times (depends on what kind of potato and how big). I'm using baby red potatoes, so I'll go for 8 minutes with 1/2 C water in the cooker. You can cut the potatoes into mouth sized chunks-- just pressure cook for only 4-5 minutes.
Then combine and let sit for a while (and hour or so is good enough):
2 C cooked potatoes, in chunks
1 tea apple cider vinegar
Later add and mix:
1/2-2/3 C mayo (or substitute plain yogurt or sour cream)
1/4-1/2 tea mustard powder
pinch of salt, to taste
2 tea shallot, chopped (or substitute red onion)
2 tea parsley, chopped
1/4-1/2 tea garlic, minced
optional: long green onion, sliced
Serve chilled. Great as a picnic or brown bag lunch (if you have a cooler).