I've never bought a new car that was actually on the lot. All have been orders or dealer trades. Pretty sure I signed binding contracts without VINs. Of course, once the vehicle is in, you sign a completed contract.
Once the VIN was known, the dealer called me, I arranged insurance, and in the case of the leased X-Trail, had the insurance info faxed to the dealership. When the car isn't purchased outright, they're kinda fussy on that point.
The X-Trail had 200km at purchase. I was already a little ticked at the dealer for delaying the pickup date twice, and just wanted to make sure the car was in good shape. I inspected it quite thoroughly in the sun before driving off. No regrets over the 200km, but next time, I might specify a maximum number of km.