Extra-virgin olive oil is the preferred choice of most Mediterranean cooks. As a rule, high-quality, high-priced, estate-bottled extra-virgin olive oil shouldn't be used for cooking, since its nuanced flavor can be destroyed by heat; use these high-end oils for garnishing foods, dressing salads, and the like. There are plenty of lower-priced, good-quality extra-virgin olive oils that are fine for sauteing, frying, roasting, and other cooked preparations. Whatever kind you're using, keep in mind a few rules of thumb for buying and storing the oil.
When shopping, look for a date stamp: the fresher the oil, the better. Many conscientious growers now put the harvest date on the label, or at least a "use by" date, which should be two years after harvesting.
The archenemies of olive oils are light and heat: don't buy olive oil that comes in a clear glass bottle or has been sitting in a sunny shop, and don't keep it next to the stove.
Refrigeration can help prolong the life of an oil; you can store a large quantity in the fridge (or just a cool, dark place) and keep a small amount at room temperature for everyday use. Lou DiPalo, the owner of DiPalo Fine Foods, an Italian specialty store in New York City, says that a bottle of extra-virgin olive oil should be consumed within three months of opening; beyond that, oxidation and rancidity can occur.
Also, buy from a reliable source, whether it's a local shop or a mail-order purveyor like DiPalo's, Zingerman's, Corti Brothers, or Formaggio Kitchen. The best importers and retailers track shipments to make sure the oil is handled with care.