Credit or debit cards are the way to go, assuming you’re not docked with a major surcharge on cash advances by your bank or provider. Those can range from a dollar to $10 or more on some credit card accounts. There are now plenty of ATMs (Bancomat).
Traveler’s Checks are old news. Personal checks are a dead end. Cash exchange outlets are few (unlike London, say) and their surcharges outrageous. Several are located on both sides of Via della Conciliazione, the boulevard that leads to St. Peter’s. You can also change cash in any bank but the waiting in line, documentation and paperwork don’t make it worthwhile.
Swallow the surcharge bullet and use plastic. (While there are still some no-credit card holdouts in shopping and dining, they’re few and far between in urban centers.
Hitting the countryside is another matter. Ensure you travel with necessary but not excessive amounts of cash. Don’t undertake a rural side-trip without each person having at least €100 cash for emergency situations).
Also, with all due respect to American Express, many Italian businesses don’t accept it. Visa’s the name of the game. If you’re dead-set on Amex, call ahead to ensure acceptance.