I'd suggest you have a look through the HOWTO's on http://www.tldp.org.
There are many on various aspects of networking.
For file sharing the usual Unix/Linux solution is NFS.
The X window system is intrinsically network transparent. Once you know how you will be able to run a graphical program on one machine with the display appearing on another machine. You can also set things up so that one machine can act as a graphical terminal (called an X-terminal) displaying a complete desktop running on another machine.
If you haven't yet done so, I would suggest you start with the most basic network application which is running a login shell on a remote machine. Today the standard applcation to use for this is ssh. Though you won't be needing its security features on your private isolated network, I'd suggest you learn to use this rather than the older insecure solutions like telnet and rsh because virtually any Internet connected host is going to be using it today. A companion program included with ssh, called scp, can be used to easily and securely copy files across machines.
In any case you'll need to get remote shell access working before being able to use remote X window apps.
You should also be aware that neither NFS nor remote X is particularily secure. They're generally used natively only on private secured LAN's. X can be used securely across the Internet by running it through ssh, which provides specific features for this.