The best oil to caramelize onions is olive oil which has a lower smoke point than canola and is perfect for caramelizing onions.
To allow the caramelized onions flavor to shine you want to use a neutral oil which can be canola oil or grapeseed oil that also can withstand high heat without smoking.
Olive oil can also tolerate high heat and is a great choice for caramelized onions.
Butter is not ideal for caramelizing onions as it burns more quickly than olive oil although the butter does add flavor.
You can also use both butter along with olive oil and the butter will add flavor to your caramelized onions and the olive oils higher smoke point prevents the caramelized onions from burning.
When caramelizing onions you can also use a pinch of salt to draw out the liquid from the onions, which helps the onions soften.
To make caramelized onions at home start by heating the oil in a 12-inch cast iron skillet over medium heat.
Add the onions and sauté for 5 minutes, or until starting to soften.
Add the salt, reduce the heat to medium-low and cook for 50 to 80 minutes, stirring the onions every couple of minutes, or until the onions are very soft, golden brown, and caramelized.