How do I get started as a computer artist?

If you want to stick to Linux, then you should definitely use Gimp. Gimp isn't really the most user friendly because of its interface, but if your using Linux to begin with: its the least user friendly OS out of all three. (Three being Mac, Windows, Linux) In my opinion, whatever can be done in Adobe Photoshop(windows, mac) it can done using Gimp(linux) as well.
If you are used to painting on a canvas then I will most definitely recommend a wacom tablet. Check out this website for more information: http://www.wacom.com/intuos/
Using the mouse to paint is simply just not traditional and very difficult to get those beautiful strokes with the wrist. Wacom Tablets also have sensitivity pressure on the pen, that is similar to a pencil/paint brush. It is the closest thing to holding a paint brush, pencil or pen.

Now the question is, what kind of artist are you? What kind of art do you paint on your canvas? Landscape? Matte Painting? Architectural? Human body? Fantasy? Sci Fi? Anything can be done with the right paint program.
A lot of the times a computer artist will start off with a particular 3D application, blocking the basic shapes of what they want to paint in 3D space for an accurate perspective. Then the artist would paint over these shapes in a paint program such as Adobe Photoshop/Gimp.
As a current user of Adobe Photoshop, this program has an abundance of brush options for the user. The brush can be customized to paint just like your brush on a canvas. In order to really find out what the settings for the brush do, you can read the manual and try to understand what the engineers are saying or if your like me, I personally need to get the hands on interaction and see for myself what the setting actually does. My best advice is.. Click an option, start painting and see what happens. You will find you will understand these options alot quicker and more efficiently if you Photoshop also has a variety of filters that can make your paintings on the computer look as if it has been painted on a canvas. Hope this helps.