The original Mafia 2 guides are still relevant for most of these.
This video (not mine) is really helpful in terms of the route. I failed this mission on the way back to Joe's apartment because I was booking it down the motorway and was killed on impact during a collision (so this video helped me do the run twice) So please note this mission only ends when you return to Joe's apartment, not when the stamps are delivered,
nor is there a checkpoint. I used the Jefferson during my run, the first car you own. Also, don't forget to disable the speed limiter if you have it enabled, and keep your eye on the mini map for the cops. Last thing you want is having them pull you over. This is obvious, but don't crash either...