When you cook pasta, something you have to mix the pasta in the pan with olive oil and various ingredients. For example, in this recipe: http://smittenkitchen.com/2010/02/spaghetti-cacio-e-pepe/
Afaik, there are 4 grades of olive oil, which one should I use in this case?
I've heard that extra virgin olive oil have low boiling point, and the nutrient goes away upon high temperature. I have only a bottle of olive oil which is extra virgin olive oil. Should I use some lower quality olive oil?
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:
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.
The grades of olive oil actually depend on the particular legislation of the country you live in.
In Europe it is regulated by directive 136/66/CEE, reg. CE 2568/91 and reg.CE 1989/03 (PDF).
The denomination depends on the acidity of the oil. Although the law does not specify it, you also have another characterization, based on the number of "pressings" and the strength of the press that olives had. Therefore, commercially, you have different grades of extra-virgin olive oil: first press olive oil, for instance, is derived from the first press of the olives, with 10-12 kg/cm2 force, has very low acidity and a strong amazing taste, but has a very low yeald, so it's quite expensive.
In particular, 8 grades of olive oil are defined, see page 4 of the linked PDF.
Traditionally you would use extra-virgin olive oil for this kind of recipes.
However, which one you choose goes down very much to your taste. For instance, I know someone who loves to use first press extravirgin olive-oil, but to me that tends to dominate too much the flavour of the dish (and it's quite expensive).
That said, I wouldn't heat the olive oil almost to smoking point to do this kind of recipe. I may almost use the oil a crudo (without heating it at all) just let the pasta heat it up. When the recipe requires to heat the oil up (e.g. spaghetti aglio, olio e peperoncino where you need to fry the garlic and the chili), heat it up slowly and don't let it go for too long, unless you want a burnt garlic taste, that is.
