When using oil at all for cooking (as opposed to salad dressing, say), I almost always use coconut oil - super-good for you, full of lauric acid (only other source is breast milk) and awesomely healthy.
. Butter is also good if you've started dairy, and if not, ghee (clarified butter) doesn't have the milk solids. Olive oil isn't good for high-heat cooking because it breaks down to bad fats but it's OK for pasta and I think for baking, and definitely for dressings where no heat is used anyway. If no food allergies, sesame oil is also good, and you can get it processed for higher-heat cooking. We use very little veg oil here, come to think of it.
