I experimented a lot, with mixed results. My ratios always seemed to be off, and one flavor or the other was overwhelming the salad. One day in a burst of inspiration I looked up the Best Foods recipe (Hellman's mayonnaise on the other side of the Rockies). Bam, almost perfect potato salad. I've since tweaked it here and there: the biggest change was reducing the salt drastically. So, here's my potato salad recipe.
Basic Potato Salad
3 lbs. potatoes cut into 3/4-inch chunks
1 & 1/2 cups mayonnaise
1 Tbsp. stone ground mustard
3 Tbsp. vinegar
1/2 tsp. salt
2 tsp. sugar
1 tsp. ground black pepper
3/4 cup thinly sliced celery
3/4 cup chopped onion
I don't peel my potatoes, just scrub them good, but you can if you like.
Cover potatoes with water in a large sauce pan and bring to a boil over medium-high heat. Reduce heat and cook 10 minutes or until potatoes are tender. Drain and let cool slightly - not much more than 10 minutes (this is called steam-drying, and lets some moisture escape).
Combine mayo, vinegar, salt, sugar and pepper in a large bowl. Add remaining ingredients and toss gently. Serve chilled or room temperature. I like to let it refrigerate over-night so the flavors mingle well.
You could add a couple chopped hard-cooked eggs, or crumbled bacon. You could decrease the mayo and add a good measure of yellow mustard for yellow potato salad. From this recipe you can probably figure out how Grandma did it.
Here's a picture of a batch I made in June 2011 with red potatoes.