Why put the cheese on top of the burger when half of it just melts off? Instead, form the burger around the cheese so you can char the meat and safeguard the more delicate flavors. Use any mixture of hard or semihard cheeses--Emmentaler and Gouda or Asiago and Parmigiano-Reggiano also pair well.
To oil a grill rack: Oil a folded paper towel, hold it with tongs and rub it over the rack. (Do not use cooking spray on a hot grill.)
3 1/2 medium-fat meat