Hey Max,
I am no expert, but I have done a similar thing that you are talking about. What I did was first, find the studs in the wall using a small hammer or a stud finder. That is to make sure you drill your holes in the "channel" for the wires as opposed to hitting the studs and having to drill multiple holes. Also, you may want to buy or rent a tool that will help you find out if there is any electrical or plumbing in the channel you decide to use. Once you know that all is clear, you should use an electrician's wall fish. It is a flat piece of metal rolled up like a big tape measure with a hook or something like it on the end that you tape your wiring to. I would start at the high point and fish the tape down the bottom hole given that you will probably have a smaller hole on the upper wall than at the bottom of the wall. Also, I highly recommend a second set of hands to make the connection between the top hole and the bottom hole easier. Once you have the tape connected, just attach the wires and pull the tape back to you. Do that for each connection and you are done.
Hope that helped some. I put my speakers in the ceiling and had to go through some of the same issues you are talking about.
Justin