Does he have separate network connections from the phone plugs in all the rooms? I would check and make sure that the cat 5 cable you see isn't being used for the phone connections.
Most builders now are using network cable to run the phone lines.
As for your setup, yes that would work. Modem and wired or wireless router in the main box. Run all the rooms off it. Connect wireless router in the office.
As for what router, take your pick: Linksys, D-Link, Netgear will all do the job.