There are lots of different cheeses in the world. Some, like Cheddar, comes in a wide variety of shapes and colours. Some melt well, some taste good. It can take a little experimentaiton to find your favourites for different things, but here are a couple of guide lines.
Cheddar. Mature and yellow (not died orange) cheddar melts beautifully and adds good flavour to cheese sauce, quesadillas or cheese on toast.
Goats cheese (chevre). Goats cheese has a tangier flavour than Cheddar but again melts fairly well. It’s nice toasted, chopped into salads or used in quiches.
Mozarella. Young mozarella melts very well but is quite wet so isn’t great for quesadillas or cheese on toast. It is wonderful slices with tomatoes and basil, or torn into pieces and added so pasta or vegetable bakes. Mature mozarella also mets well and usually comes ready grated. This is good for pizza, but doens’t have all that much flavour.