Is it cheaper to buy a home at auction, short sale, regular sale or doesn't make a difference?

[Think_about_it]

For example if someone has enough cash to buy a house outright without bothering with a mortgage, what's the best way to go about it? If they buy at auction, are there a bunch of fees and back payments from the previous borrower that are tagged on? Do only the least desirable homes that weren't able to sell through a short sale go to auction? Any insight would be appreciated!