Depends on the food. Tonight, I used three different cooking techniques for my dinner: Poached salmon, steamed kale and sauteed samphire. And yes, it was epic.
I fry beef steaks in beef dripping and pork in lard. I grill sausages and pork belly slices. I steam cabbage with olive oil, garlic and water. I sautee mushrooms in even more butter and even more garlic.
Basically, I go with whatever method makes the food taste the best, and don't skimp on the fat where appropriate.