You're looking for a naturally produced oil like lard or tallow, not a seed oil like corn oil or vegetable oil or any of the natural oils that are commonly diluted with seed oils, with a flavor profile you enjoy and a high enough smoke point that you won't burn it.

Mostly it is whatever is handy. Butter has a significant amount of water and a low smoke point but if you clarify it, it raises the smoke point by roughly 100°F.