Basically you need to pay attention to the "waxy" types vs. the "mealy" types. Baking potatoes, such as Idaho russets, are mealy types. Many others, such as "new" red potatoes, are "waxy" types. Yukon Golds and their ilk are in between, but lean toward waxy.
Waxy types are good for holding their shape in chowder. Mealy types are better at falling apart and therefore thickening. Traditional New England style chowders favor waxy types as they have a thin broth with chunks of potato, and a sharp divide between the two. The skins on waxy potatos tend to "stay on" better because the potato flesh doesn't disintegrate out from under them. There is no right or wrong, but I, personally, don't go for russet potato skins in chowder, so if I use those I peel them first.
Short version, you need to figure out which type your first batch was and stick with that.
Edit: The fact that you're even paying attention means you're 90% of the way there.