For frying, the oil that does the least "harm" is a polyunsaturated oil, specifically canola oil. It has a neutral flavor and is suitable for deep fat frying. Peanut oil would be a good choice as it is a mono-unsaturated oil and has a very high smoke point ( you can fry at a higher temp). Frying at a hotter temperature will cause the food to sear on the outside and absorb less oils. Olive oil is a great oil to use for salad dressings because it is a mono-unsaturated oil and of course has a good taste, but it is poor for frying (other than sauteing) because of it's low smoke point. Nut oils (other than peanut) are also good for salad dressings, but they are expensive and have characteristic tastes that you may or may not want.
All fats are 9 calories per gram, which is more than twice the calories of carbs and proteins, which are 4 calories per gram. So the real thing to do is to become aware of which foods are high in fat and avoid eating fats as a large portion of your diet. Even "good fats" (unsaturated, non-hydrogented) are bad for you if you eat them to excess, because you will eat more calories in a smaller quantity of food, and thus might overeat, calorie-wise. When possible, and reasonable, avoid saturated (solid) fats like butter and the fat on meat, including hydrogenated fats (transfats) like shortening and margarine made from hydrogenated oils.