Yes, it is something you can learn yourself and eventually build yourself to a professional level.
For starters, there's no need to go buy professional equipment. If you become really serious about it, then you might want to start thinking about pro equipment. It is all very expensive.
As with anything technological driven, times are different for every department in film making than what it used to be, so doing any kind of color correction today is much more accessible. A lot of people begin by using some of the cheaper software or plugins - some even give you many shortcuts. However, a lot of budget films are plagued these days with awful colors that just seem "cool" to people and can be done with a few clicks on your mouse. It is something similar to Instagram's filters and apparently seems to please the crowed.
To really become a good colorist you need to understand the basics of it all and play around for a way on as many projects as you can with a wide variety of tools. Learn how you properly use waveforms, understand the importance of a calibrated monitor, know what gamma space and color space is and many more. If you keep at it, you will detach yourself from the "one-click-magic" that most indie filmmakers use and be on your way to becoming a professional.
With all that being said, you can get good results even with the cheaper, beginner-class tools, pretty quickly.
