I am a European, so I have opinions about cheese. Here is my take on it, and do feel free to argue with me. Processed cheese slices are a very low-rent product, so when I buy them I get the superior Kraft-branded 'Cheese Singles.' They melt well and have the right amount of nasty orange dye in them. As for uses, there is only one application in my kitchen for these rubber squares of awful: cheeseburgers (http://noseychef.com/2017/10/04/cheeseburger-and-fries/).
For most all other applications they require a nice melting cheese that does not split when heated I use French Gruyere, sometimes mixed with Parmesan. Occasionally, I might use Emmental or Gouda, but never Cheddar (because it splits into oil and grit). For a mornay sauce, I will happily use a mature Cheddar. For pizza, of course, there is only mozzarella.
For most all other applications they require a nice melting cheese that does not split when heated I use French Gruyere, sometimes mixed with Parmesan. Occasionally, I might use Emmental or Gouda, but never Cheddar (because it splits into oil and grit). For a mornay sauce, I will happily use a mature Cheddar. For pizza, of course, there is only mozzarella.