There is a huge variety of potatoes available—as many as 5,000 varieties in South America alone!1 There obviously aren't this many in the supermarket or at the farmers' market (thank goodness) but it can still get confusing since different types of potatoes work better for different purposes.
Good baking potatoes, for example, are starchy potatoes such as Russet potatoes (including Idaho potatoes) and sweet potatoes. These can be mashed too.
If you want to boil or roast potatoes, you need thin-skinned waxy potatoes, such as red potatoes, fingerling potatoes, or new potatoes. These are good choices for potato salad too.
Good all-purpose potatoes for mashed potatoes, French fries, and potato salad include Yukon Gold potatoes and even blue or purple potatoes.2
Choose firm potatoes without "eyes" (potato sprouts) and definitely do not buy any potatoes with a green tint. The greenness comes from the toxin solanine, which is produced when potatoes are exposed to light and can cause vomiting, diarrhea, headaches, seizures, and in extreme cases, coma and even death if ingested in high enough quantities.
Store potatoes and sweet potatoes in a cool, dark place, and never put them in the refrigerator. At cold temperatures, the starch in potatoes is turned into sugar, affecting their flavor and texture.3
The nutrition DNA of potatoes. For example, you can see that 1 potato covers 65% of your daily need of Manganese and 46% of the recommended Copper intake. Hover over the bars to see which nutrient is covered.