I cut and then emboss because if at all posssible, because you could smoosh down the embossing when cutting it, if that makes sense.....well now that I read your question again, are you talking about embossing folders or powder embossing? I stamp first then cut, then emboss. If I am embossing an image with powder, I would emboss then cut. Does that make sense???
As far as digi stamps, I use copics with the stamps. I don't use many digital stamps but I have a couple. I just make sure to use good paper when I print and then I make sure the image is completely dry before I begin coloring.