Need cooking oil advice: food allergies

I am allergic to nuts and I have severe migraines when I have coconut so likely something there too.

I am cooking more from scratch to control what I'm eating.

I currently have a decent bottle of Extra Virgin Olive Oil. I also use butter sometimes for sauteing.

As I said I can't do nut oils or coconut. What are some good basic affordable oils that won't destroy my health? I hear horrible things about the seed oils. But maybe they're not that bad?

Thank you.