You also have to check your allergies. If you are allergic to nuts, nut oils won't be for your face either. Coconut and cocoa butters are higher in that pore clogging scale so I would not recommend that on your face. Oils should be ideally be extra virgin, cold pressed. You'll have to experiment on the texture you want from an oil and the type of skin you have. Light oils like sweet almond and jojoba and grapeseed for a light moisturizer is great. Avocado oil and emu oil are good for dry, more mature skin. You can use olive oil to remove makeup. I am very partial to a mix of jojoba, sweet almond and shea oil on my face. I use it at night and it leaves my face amazingly smooth in the morning.
If you were hinting on using cooking oil like canola or vegetable or corn, it wouldn't be my choices.