[gwilki]

As others have said, many hobbyist machines are capable of doing what you want. I suspect that your biggest expense will be software. I am only familiar with Vectric software. Vectric makes good stuff - pricey, but very good. However, the only product that they make that will let you take a picture or a drawing and model it into a 3D model is Aspire. Their other products will do 3D carving but you cannot create the model in them. Once created, almost any machine will allow you to carve it, leaving a flat back/bottom to attach to your piece.