The ip address for the internal nic on the server is the gateway for the client computers.
Is there anything else besides the modem connected to the switch? If no, why not connect the modem directly to the external nic on the server and apply a firewall to that nic. Set the nic to obtain an ip address automatically through DHCP from the ISP. This would set up the internet connection for the server fairly easily. Then the server would route traffic to the external nic and out to the ISP.
You can intitiate ICS on the server which would set up NAT and automatically route any internet traffic from the clients on a private addressing scheme out through the external nic on the server. By doing this ICS will do the setting up for you via a wizard. But make sure that the server is connected to the internet and that you have connectivity from the server to the rest of the LAN. Do NOT apply File & Printer sharing on the external nic or client for microsoft networks. Only do this on the internal nic pointing to the Lan.
Remember that by sending and receiving all this internet traffic through the server you can create quite a strain on the nics attached to it. So to be safe purchase two fairly expensive nics to ensure quality and reliabilty, 3com etc.
Another way would be to purchase a decent router with firewall capabilities and connect the modem to it. Then connect the switch to the router via the ethernet port and connect the server and clients to the switch. Then the gateway for the clients and the server would be the ethernet port on the router that the switch is connected to. This would not require any extra burden on the server due to acting as a gateway for internet traffic for the clients.