Extra virgin olive oil is the best option for frying fish
Researchers have studied the changes that take place in fish lipids and in the oil during frying processes, and have concluded that using extra virgin olive oil is the best choice. Ref. Source 6u.
It is possible to burn oil. In my opinion, olive oil is the worst one to burn, the smell lingers for days. Would also suggest that getting the oil without anything added to it, also works best for frying.
EVOO is probably the purest oil as it requires very little refining for the final product.
I'm with Malcomshaw on this one. Olive oil might be the better oil but its not really good for frying. I tend to use canola oil over the others.
Edited: Stacia on 17th Jul, 2016 - 10:57pm
Stacia,
Canola is a safer way to go considering the number of people developing allergies to peanut and peanut products. However, the taste and flavor added by using peanut oil in frying, well it adds a whole other dimension to the finished fried foods.