Salt potato kits, sold all over Upstate New York, use a very specific size of potatoes; Size B, Grade US no. 2. While most grocery stores don't define their potatoes using this method, you can't go wrong buying small creamer potatoes that are one-or-two-biters. The shape of the potato doesn't matter at all.
*To test your potatoes, use tongs to lift a large potato from the boiling water. A skewer plunged into the potato should pass through the potato completely if it is done.