I use Avocado oil; it has a high smoke point and seems healthier. Other oils are OK if you don't cook on high heat (use medium heat or lower).
I use either butter or a butter/canola blend for most stovetop cooking and generally use an olive/canola blend for breadmaking, with the exception of pizza crust which is oil-free.
Also, recently I think I read that coconut oil may not be as harmful as thought earlier by some (my guess is people thought it was harmful because it congeals at a higher temperature than other vegetable oils do). But on the other hand, people in coastal states like Kerala, Tamil Nadu, etc., must be using it a lot, and I have not read about them having higher cardiac problems.
All this is just anecdotal, BTW.