Unless you wind up with very old Ethernet cards, your Network Interface Cards or NICs will probably support one or two speeds on the network, 10 megabit, 10BaseT, or 100 megabit, 100BaseT. You can recognize these cards by the square connector on the back, called an RJ45 connector. If your cards have a different connector, check your manufacturer's web site.
Unless you have a very fast leased line connection to the Internet, 10BaseT cards will do for your NICs. Cable modems only transfer at 3 Megabits/sec. ADSL modems cannot go faster than 8 Megabits/sec.
You will be connecting the computers on your GREEN network to the IPCop computer on IPCop's internal GREEN NIC. If you have ORANGE or BLUE networks then these should be connected to the relevant NIC.
If there is only one computer on your network, all you will need is a single category 5 crossover cable. You can recognize a crossover cable by holding the transparent RJ45 connectors at each end next to each other. If the wires in the connector attach to different pins at either end of the cable, you have a cross over cable. Otherwise you have a straight through cable.
Connect IPCop and your computer to each other with the crossover cable. You have just set up your simple network.
If you have more than the IPCop and a single computer on the same network, you will need to add another piece of hardware called a hub or a switch. The Ethernet protocol sends message packets to all computers on a network out of a single port, so all other computers on that network have to be able to see their packets, and be able to send packets to the other computers on that network.
If you have a hub or a switch, you will have to plug each computer on a network into the hub or switch via a straight through category 5 cables. Make sure each cable is a straight through cable by holding the transparent RJ45 connectors at each end of the cable next to each other. If the wires at each end attach to the same pins, you have a straight through cable.