Made this the other day. Grilled cheese is good with cheddar—and it is, pretty objectively, "better"—but tbh I found myself pining for good ol' velveeta.
It's gotta be cheap American cheese slices all the way, baby. I prefer real (rennet-free) cheese for almost any other sandwich, but for a grilled cheese, there's no competing with Pasteurized Prepared Cheese Product.