Unlike some traditional cuisines, you won't have to refurbish your kitchen to cook Italian food; most of what you need you should already have. Commonly-used tools include a skillet or sauté pan; a pasta pot; a cheese grater; and a colander or two.
Olive oil is a common ingredient in Italian food, but just because it's an oil there's no reason to be scared of it. It's extremely versatile, and contains the healthy kinds of fat that your body needs. It can be used as a dressing, a sauce ingredient, in baking, or as a bread spread; it's a lot better for you than butter.