2. Gorilla Glass Protection
In addition to the oleo phobic coating, you should also make sure the display has a protective layer as well. In most cases, it will be from a company called Corning whose Gorilla Glass can be found on phones in all price ranges.
As the name suggests, these panels add an additional coat of protection to absorb shocks and falls. It’s worth pointing that this doesn’t guaranty your phone won’t be damaged if the phone slips out of your hand, but it will relatively bring down the amount of the impact.
Whether a phone has display protection can be found in their specifications sheet.