Since purchasing a car is one of the major expenditures in a person's life (usually second only to buying a house), there is usually more than just one factor involved in this decision. Certainly, one would be the final price of the car. A savvy negotiator can often reduce the asking price by $1000 or more, and most dealers are flexible enough to make a deal so that the buyer does not make his purchase elsewhere. Many people have a price range that they must honor, and many buyers look for the best deal within their range. Other considerations would certainly include the size, make and model. Many people have a specific brand in mind (be it Toyota, Ford or Lexus) and this may be the most important aspect for some. Others may have made up their mind on a specific model (such as a Ford Mustang or Volkswagen Beetle), and this may be their #1 consideration. Other buyers may simply want a large car for various reasons; for very tall people, such as basketball players, this may be the most important aspect of a purchase. Small, gas-saving economy cars are most important to other people. For some people, safety is a prime consideration. Cars such as Volvo, with excellent crash protection histories, may be the prime focus for such a person. A new trend includes environmentally conscious autos--cars that use either alternate fuels or hybrids (such as the Toyota Prius) that do not rely as significantly on gasoline.
Of course, this will differ greatly depending on the person answering. For me, when I go to buy a car, I know what size of car I want and then I look for something that is going to give me good value for my money.
Specifically, I look at the car ratings, particularly in Consumer Reports. I want a car that is going to be durable and reliable. I do not want one that is going to be needing repairs all the time and I do not want one that is going to have safety issues.
What I care about is really quite boring -- I want a reliable, safe, utilitarian car for a good price. I don't care about style, power, things like that.