"Commonly used" depends mostly on the culture, I'd assume. There's a lot of different oils, so I've organized by use rather than try for a complete list.
Some of the ones that you might find in a "typical American" foodie's kitchen include:
For frying: something with a high smoke point : peanut, sunflower, soy, extra light olive oil
For baking (muffins & cakes): something with a mild flavor : corn, canola, "vegetable", soy
For baking (biscuits & pastry, or greasing a pan) something solid at room temp : butter, shortening, lard
For general pan cooking: olive oil (any kind), butter, anything from the "baking (muffins)" list. update: this assumes sautéing heat or lower; see 'frying' for higher heat applications.
For salad dressing: any nut oil, mild oil, or virgin / extra virgin olive oil
For sauces: Butter.
For finishing: something flavorful to drizzle over at the last second... odds are, it's extra virgin olive oil, but possibly sesame or a nut oil.
Now, there's regional differences -- in the south, it's pretty common to save your bacon grease for cooking and to use shortening for frying. Lard's still popular in hispanic (and likely other) cuisine, schmaltz (rendered poultry fat) is used in both Jewish and French cooking. Ghee (similar to clarified butter), is used Indian cuisine ... and the list goes on.
If you're looking for a 'must keep on hand' list -- a mild oil, extra virgin olive oil and butter will get you through most anything. Add shortening if you like baking, and sesame oil if you like to cook asian food, and you'll be prepared for most anything.
For this dish, you'll probably want to use a low-end extra-light oil (since it's being heated quite a bit), and then drizzle in nicer extra virgin oil to finish the flavor after the pasta has been tossed into the cheese, oil, and spices.
The rule of thumb is to have two kinds of olive oil:
- High-grade, richly flavored extra virgin olive oil (for finishing)
- Extra light, not extra-virgin olive oil for use as a cooking oil. You can use a cheaper oil for this -- many people choose to use a later pressing, crudo or "pure olive oil" (in the US) kind.
The high-end oil is for adding it to sauces and drizzling on mostly-finished dishes to add that rich flavor. You're looking for something with a lot of taste, and it's a good idea to get small amounts of pricier oil. Getting small bottles means you'll be using fresher, more flavorful oil because it hasn't been open for long. Plus, you won't need much to finish dishes. Note that for this use, you want to add the oil near the end of cooking, as heat will alter and weaken the flavor.
The low-end light olive oil should be of neutral or light flavor, and will be more tolerant of heating than extra-virgin. Because it has a much higher smoke point than extra-virgin grade oil, use this in recipes calling for heating up olive oil. If necessary for flavor, add some of the good stuff near the end of cooking.
Best Answer
No. Steak needs be seared at a high, high temperature. Not only would extra virgin olive oil lose everything that makes it special at such a high temperature (so not worth the expense anyway), it would also burn. The smoke point of EVOO is 350F, 180C (give or take). That's simply way too low for searing steak.
There is no such thing as a cooking oil that's hot enough to heat to what I would consider ideal steak steak searing temperature.
(I just used this picture in another answer, that's Celsius by the way)
No cooking oil can withstand that kind of heat. So how can you get away with it? Well, when I do it, first I remove the batteries from every smoke detector in my apartment and open my kitchen windows. Secondly, I choose a very refined (read that tasteless) oil with a high smoke point. By using a refined, tasteless oil, there's really nothing left after it burns to taste nasty; it just tastes like char, something I want anyway. Third, I don't put oil in the pan, I just lightly oil the steak. The method works great, but it requires a cast-iron pan and a high smoke point, neutral oil.
I'm not crazy about Jamie Oliver's method because I like a serious char. You can tell he's not using extreme heat, because he's using a non-stick pan. I assume he doesn't throw away the pan with every steak. Even with his method, EVOO would be a bad choice of oil. The point at which extra virgin olive oil gets nasty is significantly lower than the temperature that will ruin a non-stick pan 400F+ (200C+), and much lower than the temperature necessary to get a decent char on a steak. Refined (pure, or extra light) olive oil would be an OK choice, as would canola, safflower, refined avocado, grapeseed or soybean.