Advice needed regarding Future car purchase?

Im looking to buy a used car soon and im not sure what a good down payment would be on a $27,000 car. Im planning on putting $7,000 down, would that be good enough and finance the rest or should i put more into it? What kind of negotiation leverage would i have on the dealer if i showed up at the dealership with $7K Down, 772 Credit score and research from Galves and Nada car values? BTW, the vehicle im looking into is a 2006 Lexus GS300 with 48K miles. Dealers have this car selling at $30K+ but according to the research ive done, the car is worth $25K-$26K. Advice would be greatly appreciated.