There are two big variables to consider when picking out your cooking oil. First, you want to be aware of the smoke point of the oil. The smoke point is the temperature at which the oil, or fat, begins to smoke. If you've ever forgotten about oil on a hot pan and then it starts smoking, your eyes burn, and it smells terrible, that means that the oil has exceeded its smoke point. These oils become rancid and may be harmful to your health if consumed over time. As a general rule, you want to choose oils that are appropriate for your cooking temperature.
Second, you want to consider the composition of the fatty acids of the oils. In short, omega-3 and omega-6 fatty acids are essential to our health. We can't MAKE them ourselves. We must consume them in our diet. The typical Western diet is very high in pro-inflammatory omega-6 fatty acids and relatively low in anti-inflammatory omega-3 fatty acids. We ideally want our omega-6 to omega-3 consumption ratio around 1:1 or 2:1, but it's generally much higher than that. While we need inflammation as a barrier to infection and injury (we couldn't survive without it), too much of it can contribute to a whole host of chronic diseases that are common today.
Oils that are heavy in omega-6 fatty acids include safflower oil (133 omega-6:1 omega-3), sunflower oil (40:1), corn oil (83:1), peanut oil (32:1), sesame oil (138:1), and grapeseed oil (a whopping 676:1). These oils are already in so much of the processed foods that we eat. If you don't already notice that, start reading labels when you're at the grocery store. That's one of the many reasons that I'm an advocate for cooking at home! If you do that, you have complete control over which oils you use.
This site is a good reference for smoke point and fatty acid content.
Full disclosure on the photo: I just ran out of coconut oil and used the oil that I rub on my face and under my eyes in the photo (not like it really matters, because I can still cook with it!).
Please comment below if you have any questions on this post. I may do a follow-up post in the future that delves into more details about specific oils. Enjoy your Cinco de Mayo, and remember to read your food labels and pay attention to smoke points!