It's called a switch. Many wireless routers have a 4-port switch. Also you can purchase a switch separately.
Switch for small LAN, Router for two or more
For a small LAN network, a switch is best. To connect two or more LAN networks, a router is required. (2) From Jean Andrews CompTIA A+ sixth edition (page #852): You can use a crossover cable to connect to computers without a switch or hub making it the simplest network of all. For two or more you will need a switch, hub, or router.
for small LANS use a switch, for two or more a router is needed
Connecting different networks requires a router
Yes, but the data traffic will traverse the Internet to reach that public IP address. If the server has another network interface in the same subnet as the connecting device, you can constrain the traffic to the LAN. If the connecting device is instructed to use the public IP address to reach the server, the traffic will first travel to the LAN gateway, which determines the best route for the traffic to reach public addresses. Typically, this would be via an ISP that the gateway is somehow connected to. Please specify your goal in your question to get an optimal strategy as an answer.
The standard is Cat-5 cabling. It really depends on your needs but for a small LAN cat-5 will suffice.
gateway
It's easy to use.
LAN
Same device----> crossover cable Different device->Straight through cable
I use LAN
Balance