A lot of people like avocado oil for it's high smoke point and nutritional properties.
I depend of coconut oil for hair treatments. Both are also great for cooking.
A lot of people swear by olive oil, especially EVOO. There's a reason Mediterranean skin is as gorgeous as it is.
"Pulling" oils and different substances is glimmer. Don't bother. There's no science behind it. Eat a normal, relatively healthy diet and you'll get everything you need; use doctor's labs to determine any specific imbalances.
We mainly use Smart Balance oil which is a blend of several oils. Olive oil is mostly for flavor, although as Americans, we're afraid to use it for anything else. I use canola oil on the barbecue grill to keep things from sticking as it handles heat better.
Oh, wait, you're asking about skin care, not cooking. Never mind. I guess coconut oil is best for that.