You usually want to use a lube that won't attach plastics. ATF is a good choice. Standard motor oil is not safe for all types of plastic.
You also want to avoid getting the lube on the top 4" or so of the cable if possible. Over-oiling can cause the oil to be pushed up the cable into the speedometer mechanism and make it act up.
The cable in the center can usually be removed form the sleeve it spins in, so it makes it easy to clean and lubricate.
Currently Running Stable:
2010 Honda NT700V
1986 Shadow 700
1986 Honda Trail 110 (Postie Bike)
1987 Honda Rebel 450
1973 Honda Mini Trail 50