As Athiril said, color conversion (big steps in color balance) is far more important to do than color correction: the more minor filtration changes that are often needed to tweak something's balance to "perfection."
But I consider shooting in shade or overcast weather to be major deviation from the film's color balance that warrants at least a stop of overexposure if filtration is not possible at the time. If you want to use filters, I think at the very least, everyone interested in shooting color film should have an 80A filter, an 85 filter, and at least one of each in the 81 and 82 series (for minor warm or cool CC changes on top of the 80A or 85 color conversion filters). A 30 or 40 Magenta filter can help too, in green fluorescent light, though many fluorescent lamps are not green now. A heavy 81 series filter is useful too, when the 85 is too heavy (e.g. cloudy/bright weather or light shade). A 10 or 20 Magenta CC filter is good when a lot of light is bouncing up from grass onto a person's face, to prevent a jaundiced look. A polarizer can be very useful if not overuse, but that is a separate issue from color balance.
It can also be quite helpful to have the same compliment of filters for your flashes. Except instead of magenta for fluorescents, it should be green to match the flash to the ambient source. The most common application would be to use an 85 gel over a flash when tungsten ambient light is also present. (It is my most-used trick at wedding receptions.) If you don't do that, one light source is always cool or warm, while the other is neutral...or worst of all IMHO, a compromise between the two. Yuck!