Let's answer the premium versus regular gasoline question first
The answer would be it depends. If your car is a high performance vehicle recommended for premium gasoline, then premium gasoline is better for your car. Will your expensive premium engine bust if you use regular? Most likely not. Most modern fuel injection systems adapt to the lower octane fuel by adjusting fuel mixtures and timing accordingly; however your engine will likely ping (preignite) and knock (sideways closure of valves or valve chatter). There will probably be long term ramifications in continued use of regular gasoline where premium is recommended, but in the short term, regular gasoline will not hurt You will lose some horsepower, but the trade off is your decision. A car that doesn't have a better fuel stipulated should be fed regular gasoline. It can drink premium, certainly, but you will lose efficiency. Higher octane gas is not, by default, better for your car.
The question of brands is a little bit trickier
Does Chevron, or any other brand for that matter, sell better gasoline for your car? The short answer would be no. The differences between brands are the additives mixed into the fuel that act as detergent to clean your engine and remove potential deposits on an engine's valve. It's true that some brands might sell gas that is better at cleaning your engine, but all gasoline brands must meet the Environmental Protection Agency's standard for detergent additives. Tests are periodically done at the pump to ensure that the fuel being sold meets minimum octane ratings for regular, plus, and premium gas. So if you pump up at a bargain gas station, its gas will not adversely affect your car. But that doesn't mean bargain gas is the equivalent of brand gas. A number of auto manufacturers have worked together to create a standard known as Top Tier Detergent Gasoline. They claim that their engines require higher standard gasoline. The companies include: Audi, BMW, General Motors, Honda, Toyota and Volkswagen. Companies like Chevron and Shell have met the Top Tier Detergent Gasoline standards. For example, Shell claims that its nitrogen-enriched gasoline is superior in cleaning engines. Do these brands sell better gasoline for cars? The subject does not have a clear answer. The AAA contends that any brand of gasoline is safe. And so far, no auto manufacturer has voided warranties for not fueling up on Top Tier gas.