Oooh, online... I misread the title, I was gonna suggest any supermarket you wander into!
My dad came to visit this past December and we did buy some cheeses from the supermarket
By some, I mean quite a few! Starting with gorgonzola, which he loves the most. So, if you find a good online place to order Italian cheese from, definitely look for gorgonzola! It's what the French call "blue cheese"
Another good pick would be parmiggiano reggiano. I don't think anyone else makes it the way Italians do
It's parmesan cheese, in translation, and its sooo good! You can add this to anything, on top of a pizza, on a pasta dish, I even add it on top of paninis
As a suggestion, when looking for good cheese, look for the DOP kind. From
wikipedia: "DOP Italian cheeses includes all the Italian cheeses which have Denominazione di Origine Protetta ("Protected Designation of Origin"), or DOP, status under European Union regulations". Which actually means quality stuff