I deep fry in peanut oil (it's expensive but if you must deep fry and want to use a fryer and therefore probably want to avoid the ballache of emptying and cleaning a solid fat it's what I'd recommend from a health perspective).
I rarely deep fry my food, but when I do I just use canola oil. I know it's not good for me, but I don't do it often, maybe twice a year. My go to oils for cooking in a skillet are avocado oil and olive oil, depending on what I'm making. I like to use butter to cook eggs, onion, to grill sandwiches, burritos, gyros, etc. For stir fry I use sesame oil, but I don't buy it very often because it's kind of expensive for a small bottle.