You can use grated Mozzarella, which is how I always used to do it. Now I tend to dice it as I like getting a bite with a small chunk of melted cheese in it. It’s good with meatballs or meat sauce; just use what you have.
I gave quite a variance on the cooking times as I’ve seen recipes (and cooked the pasta) at both ends of these ranges. The longer cooking times had more sauce I think and gave a firmer texture in the end.