I actually use Inkscape to cut. I wouldn't recommend it for a beginner as it is pretty basic and requires you to have a pretty good idea of how the system works. The main reason I use it rather than Signblazer is signblazer does not have an overcut option and the Inkscape feature does.
As for your cutting issue with it cutting the entire design for each color, that's due to how you vectored it in Inkscape. When you vector using color in Inkscape, it layers scans of each color over, with the color on top the hiding the other colors. If you uncheck the "Stack scans" option it will separate out the colors. However this will also leave a gap between colors and generally results in a pretty crappy trace. The other option is once your trace is done to manually edit the image and subtract the layers in order to get only what you want shown in each color. This can be rather tedious and involves duplicating some layers then subtracting them from others. It is different for each image so the only advice is to play with Inkscape and get to understand the various tools under the Path menu.