Coconut oil..... It's a myth that using olive oil and vegetable oils r healthy. Olive oil is good for u but not when heated, so reserve that for salad dressing. Label should say virgin and cold-pressed. Best oils/fats to use with cooking r organic butter (kerrygold) and coconut oil. Because they r saturated, they won't turn rancid with heat like other oils.
For What Purpose. the best oil is dependent on exactly what you intend to do with it. Frying, sauté and flavoring may require different oils. I don't think that you ca say that there is a best one.