For the ultimate combo, do this: 2 parts Oaxaca or Mozzarella, 1 part Monterey Jack, and a sprinkle of sharp cheddar for flavor. Throw in some pepper Jack if you like heat.
Cook it low and slow in a buttered pan. Let the cheese completely melt before you flip. If you flip it too early, you get a cheese-heist—it all escapes onto the pan.
Truth is, the best cheese for a quesadilla is the one you have right now. But now you know the rules. Bend them, break them, but never use pre-shredded Swiss. Ever.
Go forth. Get cheesy. Be happy.