If I wanted to coat an entire driveway with smoke, what s the best tactic and how much will it cost?

Using dry ice will make the results critically depend on air humidity and the light water vapor fog will evaporate and drift easily.
A smoke machine will still require still air - possibly only available early morning or at night - but the heavier smoke will stay in place longer and obey direction better. Make sure in talking to people who rent the machines and supplies that they know you will be outdoors.

Smoke machine probably, I'd hate to imagine how much dry ice something like that would take.