First of all, you picked the right distribution to learn; Slackware. The startup scripts are readable and understandable.
As you start adding packages to your linux server(s), remember that www.slackbuilds.org
is your friend.
For network management/monitoring, I would suggest looking into cacti and nagios... then pick one. It will be an effort to setup and learn about either one.
Also look into Oracle's VirtualBox. You can setup an entire virtual environment on one computer and save a bunch of electrons.
As to the network layout, that will depend on what specific thing you're learning about; routing/firewalls, LAN services, client configuration, etc.