We use both butter and olive oil on a daily basis. Butter tends to be used more in the north of Italy and is always unsalted. It can be simply stored in the fridge but of course you should watch the sell-by date. In addition, I suggest you stock at least three different oils which, with the recent influx of oils onto the market, is not difficult to achieve.
Firstly, a seed oil, like sunflower oil, is good for frying. If you have to fry fish or other food which has an unmistakable taste and smell, it is preferable to use oil which you can discard after use. Secondly, a pure olive oil should be used for the base of sauces and for frying certain foods where you want to retain the sweet taste of olives. Thirdly, you should keep a really good extra virgin olive oil. Italian is best because you can rely on it being really virgin and because of its aroma, typical of the area it comes from. The further south you go in Italy, the more intense the oil becomes in taste and texture. However, good-quality extra virgin olive oil should not be used in cooking as this flavour is lost. This type of oil is ideal eaten raw on salads or as a condiment on warm food.