I do not think it is a good idea to connect custom device to the corporate/school network, because any incorrect configuration of your TWR system may corrupt network and affect your neighbors ability to access internet.
The good practice is to have two network controllers in your PC workstation - one for public (school) network and another - for your custom networking devices debugging. It this case you can connect your TWR board directly to your PC via crossover cable and assign IP addresses as you wish.
Of course, if your network administrator explicitly allowed you to connect your TWR board to his corporate network (school network), than you can do that. In this case I think if will be a good idea to ask network administrator to assign fixed IP address for your TWR system in his DHCP server setup, so the address will not change from day to day and will be always known. This will also allow you to configure this ip address statically in your TWR settings without using dhcp client.
