What is the best oil to use to season cast iron frying pans?

Oil is used to season cast iron cookware, not clean it. Seasoning is performed with any type of cooking oil or fat (shortening, lard, etc.) Just coat the cookware entirely and place in a 350F oven for at least an hour. Repeat as needed to build up the seasoned layer.

Cleaning should be done by rinsing immediately with hot water. If stubborn stuck-on food becomes a problem, use coarse salt and a non-metal scrub brush.

To remove rust use the cut end of a raw potato as a scrubber with Comet or Ajax type scouring powder. Then re-season the cookware properly before using it.

Mild dish-washing liquid is okay for occasional use.

Always dry thoroughly before storing.

If the cookware has not been fully seasoned, a thin coat of oil after washing is sometimes used to protect the surface before storing. The entire cookware must be covered with a towel to prevent dust sticking in the oil. (It's much easier to just fully season it.)