When we ran ours, we bought a bunch of 100 foot CAT5 cables. We then went into the attic and ran them down through the walls. You dont need some special cable, you just cut the ends off and solder the bare wires into the connector in the wall plug. Works pretty well. Takes a pretty good eye, but its not overly hard.
To get from wall to wall, you basically have to run the wire through the ceiling or subfloor. Not an easy task. Find out if the house has wiring conduits. When we build our house, we had the plumber install piping (3", IIRC) running from attic to cieling in several places that was open on the ends and has a hole cut for easy access. The pipes are placed in out of the way places (no gaping holes in the living room wall
). That way, when we want to run wires for this (or cable, or whatever), it is easy to drop the wires down through these pipes.
Wiring isnt the easiest task, it takes a good bit of time and patience. Once done, however, it is very nice. If you are only doing this for internet, and dont want to go through the trouble of wiring, you could always go wireless.