For me it depends on the style of pizza, and toppings.
If i'm doing New Jersey Boardwalk style, I HAVE to use sharp cheddar.
For BBQ chicken pizza, smoked Gouda and mozzarella or Gouda/mozzarella
Philly steak pizza mozzarella, provolone, and any sharp Italian cheese at hand.
When it comes comes to fresh mozzarella, I only use it when baking on steel with the broiler element in use, so 3:00 min - 3:30 min bake times.
In regards to quality, I use the best that's available to me, some are blessed with Grande being readily available, while others like myself are not as fortunate.
My favorite brands are Stella, and Belgioioso. Love them to death.