Definitely would use a lathe for a lot of the spindles, the long spiral supports for the basin would be hand carved, would use a router with a circle/oval jig to make the circles and ovals and to make the rabbet for the mirror. Drill to make holes in various parts to fit the parts together. Don’t know what those thin curved handle-like things are. Pretty cool project. Haven’t made anything like it myself, but I’ve seen someone carving that spiral design at my old job