While crisp, thinly sliced fried potatoes layered between melted slices of cheddar and American cheese on sourdough is a great place to start, that's hardly the end-all-be-all.
You could try it with potatoes fried in olive oil, rosemary, and garlic or spicy potatoes fried with chili oil and red pepper flakes. Twice-fried French fries could also work.
In addition to the many variations of potato, you'll also want a melty cheese and decadent bread choice to complement your fried potato and cheese combination.
Classic bread options are Texas toast or brioche, but for the adventurous, sourdough, wheat, and marble rye bread will also work with the right cheese and fried potato combination.