This is a very common question and many different people will have different answers.
First, I like to seek out what the engine manufacturer recommends as they have spent hours and many dollars determining the best gasoline octane rating to put in your lawn mower engine. Gasoline is pretty much the same except some companies put different additives in it to help it burn cleaner and keep your engine parts such as your fuel injectors clean as well.
What we are concerned about is the octane rating for the gas. There are normally 3 or 4 different octanes at your local gas station. You will see 87, 89, 91 and 93. 93 would be referred to as Premium and some people swear by using Premium in all their small engine equipment.
What fuel you use in your lawn mower is decided by the compression ratio of the engine. In a high compression ration such as 12:1, you would use Premium gasoline to prevent the engine from knocking or pinging under a load such as driving your car up a hill.
Most lawn mower engines are low compression engines, so 89 octane gasoline is perfectly suited for them and will provide the most power for this application. So, save your money and buy 87 and if you have access to non-ethanol gasoline, opt for that instead.