The answer is, it depends. You need to try the tools out and see which ones fit your style. Personally, I used Gimp and Inkscape together for years. Then I bought the Adobe suite and realized, I preferred Gimp and Inkscape to Photoshop and Illustrator. I also tried a few other Open Source products such as Pencil, Synfig, Paint.net and many more. They were all great tools but I just kept going back to what I knew in the end.
I like to create the base graphics in Inkscape, add detail in the Gimp and, as of late, I have been using Spriter to animate it.
I would suggest you stick to Open Source at least until your art starts paying. Commercial graphics programs cost too much for a hobbyist in my opinion.
Also, if you have access to a touch screen or usb connected tablet, MyPaint is a fantastic digital painting tool. Check it out.