When I understand your situation right , then:
You can install a Proxy Server on your linux box and enter the Proxy in all your clients..Or you can setup a "transparent Proxy" which is completley transparent to the clients, and you don´t have to enter the proxy in your clients.
With the proxy configured, all clients MUST pass the proxy , and the proxy will "download" the requested page and send it to the client (and the proxy will save a copy on its harddisk/memory for faster access when the same page is again requested)
Many environments have a transparent proxy for accelerating the HTTP Access for the entire network. At the other side of the knife , you cant access directly services with a proxy (POP3,SSH for example)....
Have a look at
www.squid-cache.org...I´m sure you will find the squid package at your Linux CD´s too.