Pecorino romano, parmigiano reggiano, and grana padano?

Parmigiano is a cow's milk cheese and is a DOC product which means that you can't use that name if it comes from another region. Grana is a similar cheese from the same region. "Padana" refers to the entire Po valley.
Pecorino is something else. It's a sheep's milk cheese (not DOC) and you will find local pecorino in Lazio, Toscana and Sardegna---the latter having kind of a unique flavor---pecorino sardo.
How you use them is up to you as there are myriad ways.

All three similar hard cheeses. Many like to grind or shave and serve on pasta or salad. I like the Tuscan method of chopping bite size chunks and serve with a drizzle of good balsamic.
Which one? Depends on your taste.
I prefer the parm-reg.