I use Mom's basics for potato salad. Mayonnaise, mustard, sweet relish. But potato salad is already soft, so I like the added texture of finely diced celery and onions to add a crunch. And if I do cucumbers, they are sliced on the side, crunchy, not wrung out.
While not an staple in our household, I find that potato salad goes very nicely with just about any meat. I especially love it with a teriyaki or BBQ'd meat that has a sweetness to it, but I find it goes nicely with just about any kind of meat as well. Mom even put leftover potato salad in my sandwich for lunch. I always found that odd too, but my husband said, "That sounds good!" so he may get some in his sandwich tomorrow.
I started with four small potatoes that I cleaned with Fit and a scrub brush. I then quartered them and covered them with cold water. Mom would make a bunch of potatoes, but I found that these four small potatoes yielded enough to serve 5-6 people. Boil them until they are toothpick tender. I also hard boiled two eggs. I always bring my eggs to a boil then simmer for 20 minutes even though I've been told it should only be 15 minutes. They never get that grey color that indicates overcooking, so it works for me because I want my yolk cooked through. Perhaps it's the high altitude.
The key to a nice peeled egg (not that it matters here) is to dump out the hot water immediately and run your eggs under cold water. This serves two purposes. The first, of course is to stop the eggs from continuing to cook. The second is that your egg will actually condense a little inside its shell. Crack around the egg while it's still warm, let some cold water run into the cracks, and give it a swipe. The shell will peel right off. Wait too long and the egg cools down too much. The shell will stick to the egg white making it a painful peeling experience.
While you wait for your boiling pots to do their thing, in a large bowl combine 1/4 cup of mayonnaise plus 2T, a tablespoon of yellow mustard and 3 tablespoons of sweet relish. Mix well. Add to that, a 1/4 cup of finely diced white or yellow onion and 2-3 stalks of diced celery.
Once your potatoes are done, drain and add a tablespoon or two of vinegar to the hot potatoes. Doing this while they're hot allows them to soak up that flavor. I used seasoned rice vinegar (the kind you use for sushi), since I always have some on hand in the fridge. Let them cool down, and then peel and dice them into bite sizes. I've never known why you leave the skin on, then peel. It's one of those things I've been meaning to ask about... Surely Alton Brown could give me a very meaningful answer, but let's just say it's they way I was taught so it's the way I do it! A rough chop on your boiled eggs will do the trick. Toss all of that together with your mayo-mixture then season with salt and pepper to taste. Your potato salad should have a nice salt to sweet relish ratio that compliments, not competes with one another. I always finish with a dusting of paprika because it looks so pretty on a potato salad. Wouldn't this salad look nice with some crunchy sliced cucumbers around the edge?
Remember, a potato is porous. The longer it sits in all those flavors, the better it tastes. Hope you enjoy!