If you are just learning, then get a decent GPU (Radeon RX480 or Nvidia GTX1060 as a base level) and download Davinci Resolve Free edition.
V14 is still in beta and buggy, 12.5 is stable and very good , but 14 is a lot faster.

Then go get some introductory tutorials, and then buy The Color Correction Handbook (https://www.amazon.com/Color-Correction-Handbook-Professional-Techniques/dp/0321929667/ref=sr_1_1?ie=UTF8&qid=1495443334)

Colour correction really requires a lot of different skills, studying colour science would be a good idea, and to do it properly, you will require a separate broadcast monitor, output card and calibration probe.
But to get into it, a Mac or PC, a decent GPU and the free version Davinci Resolve (that used to cost Ninety THousand Dollars!) will let you use the same tools as the professionals and see if it is something you want to get into.