What type of onions please. Yellow, sweet, or white?

Generally speaking, yellow onions are the preferred onion for making soup, unless the recipe is developed specifically for sweet onions. Otherwise, your final product can end up too sweet. White onions tend not to have as strong an onion flavor, which makes them good for salads, but perhaps not so great for a soup. Since blue cheese is a strong flavor on its own, I think you will prefer an onion strong enough to stand up to it- so use the yellow.