In order to get the best deal:
If you have the credit to get approved through dealership financing on the same day, then you will likely be able to get pre-approved from your own bank or credit union. Pre-approval enables you to determine a suitable down payment and loan amount—which can also give you a better sense of what vehicles fall in your price range.
Keep in mind: Dealerships typically charge higher interest rates. For example, a dealership may tell someone with a 720 credit score that they qualify for 5.99% interest rate, but that same person could get financing through a bank or credit union for just 2.99%.