Are you looking to free hand the drawings into the computer like you would on paper? Unless you already own or are able to invest in a Wacom tablet (drawing in a natural way with a mouse is an exercise in futility), then I would skip the "drawing software" and draw your stuff on paper. You can then scan that in (that would require a scanner, obviously) and do you coloring using GIMP or some other free pixel based software.
If you are comfortable with the bezier drawing controls found in vector-based drawing programs like Adobe Illustrator, then it is possible to draw and do everything with a mouse.
Photoshop and Illustrator (and Painter) are the industry standards for this type of work ... but they are not free. Sorry, I do not know of any free titles to suggest.
Bottom line is that you may be better off sticking with good ol fashioned paper and pencils, markers, watercolors, etc until you have the means to invest in the stuff needed to make the digital stuff work to your advantage.