|Since you have a router, the correct setup is as follows:|
highspeed modem >> router >> clients
That's with the modem plugging into the WAN port of the router and clients into the LAN ports. I am of course assuming you have a router with 4 LAN ports. If you have one that only has 1 LAN port you can always purchase a cheap 8 port switch to plug into the LAN port and then plug clients into the switch.
If you do it my way, then your network printer can be plugged into a LAN port on the switch and will be available to all LAN clients. You will of course want to statically assign an IP address to the printer that's outside the DHCP scope setup on the router. That will avoid any chance of duplicate IP's on the network.
Also, with my setup then your 2nd computer could also access the internet if you want it to. If you don't want your second computer accessing the internet simply statically assign and IP to it that is also outside the scope of the DHCP server on the router but leave the default gateway address empty. With no gateway address the PC will still be able to communicate with the network printer, and other clients, but will not be able to access the internet.
This also puts every LAN client behind the firewall.