There is a lot of great information in this thread. I'm going to try to add on a bit of what I've gathered and hopefully somebody will fill in some of the gaps I still have.
As far as bits go, when you are routing a body shape to a template you generally use a "flush trim router bit." Using a flush trim bit with a guide bearing on it sounds like it'll make life easier too. These are available with the bearing on the top of the bit (towards the router) or on the bottom. The bearing is the exact same size as the rest of the bit and rides against your template while the blades trim the wood to the exact same size as the template. When you have a bit with the guide on top you would be using it in conjunction with the template on top of the body, if you use a bit with a guide on the bottom you would have the template under the body. I believe there are also bits that have the guide on both the top and the bottom of the bit.
As far as boring out cavities in the wood, I believe most everyone uses a "forstner bit" in conjunction with a drill press. These bore out circular flat bottomed holes in wood. They also seem to leave a center mark where the center guide of the bit goes a bit further into the wood then the rest of the bit. I believe this is illustrated in Andrew's picture here:
What I'm not entirely certain about yet, is how one gets that perfectly flat bottom of a cavity when working with forstner bits. I'm assuming after the majority of the work has been done with the drill press, one would go back in with a router to smooth out the bottom of the cavity and remove the center holes left behind by the forstner? I'm not entirely certain but I'm guessing a straight router bit is suitable for this purpose? I think spiral router bits might also be suitable for this purpose?
I would also guess that either a straight bit or spiral bit used in conjunction with a plunge base would be what is used for routing out truss rod cavities as well?