So, in Spain the common word for car is "coche" (el coche/un coche), in Latin America the common word for car is "el carro" or "el auto", and the word "el automvil" is used everywhere but it is more formal. In terms of which is best or what to use is really up to you; they all are equally correct. Spanish is only one.
In Spanish, "caro" means "expensive" or "dear" when referring to a person, while "carro" means "car" or "cart." The difference lies in the meanings and usage of the words.