Use Parmigiana, Loccatelli, Romano or whatever you like but don’t think you can put it on everything because it can conflict with and overpower delicate flavors. If you really want cheese, eat a piece of cheese.
Type can vary according to the sauce but NEVER, NEVER with sea food. Grandma said that was a mortal sin. Instead of the hard grating cheeses, try dry ricotta salada sometime or maybe a tablespoon of fresh ricotta in your dish before you put in pasta with tomato sauce.