What type of lubricant/grease is most suitable for brake and shift cables?
A heavy grease may introduce drag between the cable and housing, so a light lithium grease is preferable.

Lubricants can trap dirt and grit, meaning a greased cable would work better than a dry cable initially, but soon become contaminated such that the greased cable is worse.

Using a teflon-coated cable will avoid the need for lubrication and prevent water from being in contact with the steel strands.