Shredded melting cheeses are the best to use in quesadillas. While Traditional Mexican cheese quesadillas are made with a queso called "oaxaca", here in the U.S. we often use mozzarella, cheddar, Monterey Jack, Colby Jack, and Mexican cheese blends like taco style cheese. These are delicious and flavorful melty cheeses that work well in not just quesadillas, but enchiladas and taquitos too.