Most potato cognoscenti divide potatoes into two basic categories: waxy and dry/starchy. Waxy potatoes hold their shape well, so they are good for potato salads, roasting, gratins, boiling and soups. Red potatoes and new potatoes are good examples of this.
When you want fluffy, creamy baked or mashed potatoes, go for the drier ones, like russets and Idaho’s.
There is a third category, which are all-purpose potatoes. My go-to all-purpose potato is the Yukon gold, which is has creamy flesh and a yellow color that give it a nearly buttery character.