The test drive sells the car; the paperwork decides whether you keep it. Before any negotiation, ask for three things: the registration title in the seller's name, the service history, and the last inspection document. A seller who hesitates on any of the three is answering a question you did not ask.
Check the title for liens and for the word rebuilt — a repaired write-off can look flawless and behave otherwise. Then compare the mileage against the service stamps: gaps of years between entries mean the car rested, or the odometer was dreaming. Both are worth a discount; only one is a dealbreaker.
Have the car checked by an independent mechanic before you sign. The modest fee for the inspection is the cheapest insurance in motoring, and the mechanic's report is a negotiating tool: every item on it is a line you can talk down. Walk away happy or walk away informed — never walk away guessing.