I would not use a power planer for the sides, top or back. I have used hand planes, like a #4 Stanley, and a scraper, but it is hard work and unforgiving if you take off too much. I now use a thickness sander and I am convined that it is the best way to get the thickness to within 0.2 mm or so of where you want it. I finish with a few strokes of a well burnished scraper.
If you have a cabinet shop nearby they will probably rent you an hour of time on their machine for 20 bucks or so. I take the sides down to about 0.085 (2.2 mm) on the thickness sander for Indian or Madasgascar Rosewood ( I then cut off binding strips from the sides). I take the back to 0.080 and then a few strokes with the scraper on the show side. Starting top thickenss varies with the material stiffness of each top, but generally 3 mm or so for most Engelmann, 2.7 or so for German, 3.2 or so for cedar - then you have to do additional thinning with a scraper and sandpaper from about the end of the bridge to the the lining edge on the side and the tailblock of course.