While it is very exciting to have made it through the car-buying journey, you still have to cross the finish line. There is no room for mistakes, so keep your eye on the ball, so to speak.
Safety is one of your primary concerns. If you are buying from a car dealership, things are probably pretty safe. When buying from a small mobile dealer or individual, insist on conducting the car purchase transaction at the bank. If you are taking a bank loan, then the bank will insist you do the purchase their and they will accept the title for the lien on the loan.
For many smaller cash transactions, I have done the purchases at a table in the grocery store deli or coffee shop, in full view of security cameras and witnesses. Things went smoothly as expected. But if the seller was a bad dude with bad friends hiding nearby, they would think twice and likely abandon the deal altogether before going through with a transaction they had no intention of doing.