if you have a leaky gut......unrefined virgin coconut oil. If you have cardiovascular disease palm oil........If you are young and healthy with few issues......beef tallow, lard, or bacon grease.
I'm going to start looking at duck fat for higher temperatures and pastured butter or coconut oil for lower temps.
The unrefined oil that is most stable at high temperatures that I know of is coconut oil. I use it sometimes, but mostly butter on medium heat.
I like to cook with ghee! It has a really high smoke point. I make it myself.
If you do cook with olive oil use the light olive oil. Goes to a higher heat..
I prefer coconut oil, I like that it has little to no flavor; unlike olive oil. I also hear that its a no no to cook with olive oil.
I cook with coconut oil and palm oil almost all the time. Occasionally I will get good rendered beef fat and use that too. I like the coconut and palm more, though. I stopped cooking with chicken fat and pork fat about one year ago due to their somewhat high levels omega six fatty acids that I didn't think I needed more of.
I only use olive oil in non-heating applications like dressing a salad.