Reinheitsgebot is the only argument that makes any sense for using extract. It's expensive, and not the most reliable attenuator.
Personally I only use cane/beet sugar. It's cheapest, effective, and I always have it on hand in the kitchen anyway so it's one less thing to worry about. The idea that it causes "cidery" flavors are proven false by thousands of homebrewers.
I can't see any reason why people still use corn sugar. It's expensive. It is very effective and clean, but it has zero advantages over beet/cane sugar. If you can get some for free, I would use it. But if you're paying for it, don't bother.