I say this not because you are unfamiliar with the car business, but just to save you some time. If you know what a good offer is, and know that it's something the dealer should be able to do, just lay that number on the table instead of asking for "their best deal."
Fastest and easiest car deals in my experience are always the ones where a customer knows what I can sell a car for, tells me that's what it takes to earn their business, and then we do the deal. Going back and forth with offers and negotiations is pretty much pointless in today's car market.