I agree on the no celery, GBP or raw onions rule.
I like a waxy potato, either yukon gold or red potatoes for salad. The golds get peeled and the red keep their skin.
I like a 1/2 inch or so dice.
After boiling they get a good splash of jalapeno vinegar.
Dressed with mayonnaise, salt and pepper is fine, But mixed with blackened onions is very nice esp if you let it sit for an hour or two. If it sits overnight the whole thing is brown, but tastes fine.