As someone who cooks grilled cheese sandwiches for a family twice a week, and likes to experiment, I can tell you that cheddar or gruyere, mass-produced white bread, and lots of mayonnaise, is preferred by some.

And someone else will chime in with something else. I don't know what the 'ideal' grilled cheese sandwich is, but I'm willing to wager a lot of people think it isn't made with American cheese.