Cheddar melts well, if not put into boiling sauce, and it's grated fine. Cottage cheese, cream cheese, havarti, gruyere, brie, fetta, farmer's cheese, colby, monterey-jack cheese, muenster, and the hard cheese all melt very well if they are grated fine and added slowly to the sauce while mixing. The cottage cheese should be either blended, or pushed through a sieve bevore adding.
But remember, each of the cheeses has a distinctive flavor that will either go well with your sauce or not, depending on the other flavors. For instance, I might use a mild and milky cheese like muenster in a red sauce with clams. But I wouldn't use cheddar in that sauce. I would instead use cheddar in something that had lots of pungeant flavor, either Mediteranean or Mexican, including enchilada sauce, or an oregano/basil sauce with black olives and red pepper.
So, there is no one-best cheese. It really depends on the other flavors you wish to add. And the only way you are really going to learn is just to try them with varied sauces.
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