Wiring house for ethernet

I recently bought a 4 bedroom single story house. Each bedroom and the living room has a coax cable jack in the wall from the now non-existant cable tv. (I'm on satellite tv now.) I want to run cat5e or 6 through the walls so every bedroom and the living room has a jack.

I think I can simply tie/bind the ethernet cable to the coax at the wall, and from the attic pull the coax and thus pull the network cable through the wall. I'd do this procedure for every bedroom and have each end terminate at a switch in the master closet.

I know wireless would be quick and simple, but I need security as I own my DNS, web server, mail server, NAS, etc. (yes, I know I am only as secure as my firewall and such and if anyone is interest I run Ubuntu Server with ISPConfig)

Has anyone does such a thing before? Or am I getting in too over my head? I've done some new wiring for a new construction house, but never and existing structure as extent as this.

Thanks for any ideas, help, input. :-)