Hi Patrick,
Easiest route from airport to Ardrossan is probably the coast road via Greenock fairly flat and nice views of the Clyde, and on good roads it would also be very difficult to get lost on the way.
This road can be very busy with traffic however although the roads are quite good.
If you go onto the smaller roads they quickly become much more hilly and maze like, and can be quite rough ( a keen eye for potholes, pheasants and bunny rabbits is required) but are in some lovely countryside, as I am sure more informed members of the club will tell you.
How do you get used to hills? I can't
Hope you have a great time.