"Commonly used" depends mostly on the culture, I'd assume. There's a lot of different oils, so I've organized by use rather than try for a complete list.
Some of the ones that you might find in a "typical American" foodie's kitchen include:
For frying: something with a high smoke point : peanut, sunflower, soy, extra light olive oil
For baking (muffins & cakes): something with a mild flavor : corn, canola, "vegetable", soy
For baking (biscuits & pastry, or greasing a pan) something solid at room temp : butter, shortening, lard
For general pan cooking: olive oil (any kind), butter, anything from the "baking (muffins)" list. update: this assumes sautéing heat or lower; see 'frying' for higher heat applications.
For salad dressing: any nut oil, mild oil, or virgin / extra virgin olive oil
For sauces: Butter.
For finishing: something flavorful to drizzle over at the last second... odds are, it's extra virgin olive oil, but possibly sesame or a nut oil.
Now, there's regional differences -- in the south, it's pretty common to save your bacon grease for cooking and to use shortening for frying. Lard's still popular in hispanic (and likely other) cuisine, schmaltz (rendered poultry fat) is used in both Jewish and French cooking. Ghee (similar to clarified butter), is used Indian cuisine ... and the list goes on.
If you're looking for a 'must keep on hand' list -- a mild oil, extra virgin olive oil and butter will get you through most anything. Add shortening if you like baking, and sesame oil if you like to cook asian food, and you'll be prepared for most anything.
The best is flax oil. The next best is soybean oil. The third best is liquid canola (not hydrogenated Crisco).
This is because of where those oils are listed on iodine index; which is a measure of how much an oil will polymerize. Polymerization is when oil turns into plastic and is the actual chemical process responsible for "seasoning".
Here's a whole site dedicated to this topic with more detail:
Chemistry of Cast Iron Seasoning: A Science-Based How-To
Best Answer
In practice, the major refined oils are commodity products, and the two different brands may even come from the same factory, but with different labels applied.
Still, it is possible that they are from different producers, and have a different quality standard of refining applied; one may be more aromatic than the other (which is a defect in a refined neutral oil).
The only way to know for sure is to try the less expensive brand. If it has no off-putting aroma, you have a good value.