Potato Salad

We got a Joy of Cooking cookbook for a wedding gift, and it's been a great resource through the years. It ranges from basic cooking/baking/ingredient information to gourmet food. At over 1100 pages, you can't go wrong! This potato salad recipe is the only one I use.

2 pounds red or other waxy potatoes (I have used russet potatoes, or even leftover baked potatoes)
1 medium celery stalk, diced
2 T. finely snipped fresh chives, or 2 scallions, minced, or 2 T. minced red onion (I usually use white onions as that's what I have on hand, but I have used red onions)
1/4 cup parsley ( I don't think I've ever added parsley)
I usually add 2-4 hard boiled eggs as well.
3/4 to 1 cup mayonnaise
2 T. milk or red wine vinegar (I always use milk)
I also add a "squirt" of mustard--a little goes a long way.
Boil potatoes in salted water until tender, 20 to 25 minutes. Drain, peel if desired, ,and cut into bite-sized pieces. (I usually cut into bite size pieces before I boil the potatoes. They cook faster and I don't have to try to cut hot potatoes.) In a medium bowl, toss the still-warm potatoes with celery and onions.
Stir together mayonnaise and milk/vinegar. Add the mayonnaise mixture to the warm potato mixture and toss gently to coat. Season with salt and pepper to taste. Serve at room temperature or chilled. (I always chill before eating.)