Should I buy a car on my first visit to the dealership?

You don't have to. Some people are ready on the first visit after doing their research; others prefer to test drive, gather written quotes and decide at home. If the numbers are clear and match your budget, buying the same day is fine. If you feel rushed or uncertain, ask for the offer in writing and how long it's good for, then leave. A good deal for you usually survives a night's sleep.