What I'm thinking is to some way take our existing WiFi signal that all of my old laptops have been running on for almost a year, get some kind of router to accept that WiFi signal, allow me to run ethernet out of it, then into an ethernet switch and from that point, run all of this just like the many builds I've seen around here.
The term you are looking for is "Ethernet
Bridge". Most modern routers have the capability. Good luck!
http://en.wikipedia.org/wiki/Bridging_%28networking%29