Making a decision about whether to spend the extra money on premium or superpremium gasoline involves a number of factors, some of which aren't very easily related to the composition of the gas. If you're the kind of person who spends Sunday afternoons massaging wax into the hood, your decision might not be related to chemistry.
Regular and premium gases are all mixtures, and they do differ in composition. One possible difference between the regular gas and the more expensive versions involves the type and quantities of additives such as detergents in the gas.
Another difference is reflected in the Octane rating. These are the numbers (87, 92, 95) that you may see on the price displays, or on the pumps themselves. As a student of organic chemistry you now know that octane is an 8-carbon alkane. The octane rating is not about octane content, though. Octane rating is about the combustion characteristics of the gasoline. The number comes from:
Isooctane (which IUPAC would call 2-methylheptane) is given the "ideal" rating of 100.
n-Octane (no branches) is given a value of zero.
A gas with an octane rating of 87 burns with the same characteristics as a blend of 87% isooctane, and 13% n-octane.
Note that these two compounds are related to one another as constitutional isomers. Yet they are importantly different in their behavior in the engine. While these alkanes would be hard to tell apart if your burned them in the lab, in the highly optimized systems of our cars the differences between them become significant.
In case you're curious, I buy the cheap gas. In the owner's maual for my 2003 Civic I am advised that gasolines with greater than an 85 Octane rating are adequate for my car, and that using gasolines with Octane ratings greater than 87 will not provide a performance advantage or result in a longer life for my car.