Who said, "If there were no Carl Perkins, there would be no Beatles"?
Routing of the binding and perfling rabbets, most likely, will have to be terminated before it reaches the back strip in order to hand-miter multi-line perflings into the back and butt strips.
There are a few characteristics to keep in mind when buying a router for cutting the binding rabbet. It should be light and balanced in your hand. It should have a tilt base which is necessary on the back of the guitar but not the top (of a flat-top guitar). You might have to fashion a skid plate that is wider than the one that comes with a standard machine. Note the clear plexiglass plate in the photo above. This allows plenty of room for your hand to keep the plate flat on the surface which should provide a cut that is perpendicular and square to the plate. The upper bouts of the back are a bit of a different story as the back is arched and you will need to compensate for that in the router set up in order to keep the rabbet square to the side. That's when a tilt base is handy.
Remember, there are two ledges to be cut, one for the binding and one for the perfling. Your perfling selection will have to coordinate and fit into the back strip. It may require hand work in mitering multi-line perfling to meet the back and butt strips. Also, some nice things can be done by incorporating continuous perfling into the heel cap. Be sure to have a design in mind before the binding is cut. If there is no perfling (which is the easiest thing to do), the edge binding and the back strip can just be butted (most manufactured guitars are built this way). Take a look at some of your favorite guitars the next time you are in a music store. There is no harm in copying, or modifying a design that you like.
A routing set up that can be variable in both depth of cut and width of cut requires the cutter and rollers pictured below. These are available from a number of supply houses (Luthier's Mercantile International, Stewart Mac Donald, etc). The cutter remains fixed in the router. By changing the diameter of the roller, the depth of cut (into the guitar) can be controlled. The width of the cut is controlled by raising or lowering the router base, thus exposing more (or less) of the cutter.
Pictured below is a beautiful example of perfling as an artistic embellishment. (photo courtesy of LMI website).
One of the guitars that I am working on features a cutaway. These add a bit to the challenge of assembling the sides of the guitar. The box will now have three blocks to hold it in shape instead of two, and a short section of rosewood must be bent to a tight diameter to complete the cutaway. The techniques for bending wood vary depending on the luthier's experience and equipment. Woody's method is old school (bend it over a copper pipe) mixed with some new tech in that I now lay an electric heating blanket from the LMI side bending rig to heat the rosewood. A picture is worth a thousand words.