If you have more than one host on your local network whether it's at home or a business the resulting network is called LAN. A WAN or MAN link then connects this LAN with another LAN in another location to form an internet (small i, Internet with a large I means "the official" Internet).
In the beginning a bus topology was very common and later with Ethernet switching a star topology connected most nodes on a LAN. One topology that is not listed is a mesh and/or partial mesh. A mesh means every node on a LAN connects multiple times to other nodes, traffic may go through any link not just the one connecting to a centralized hub.
You can use an RFC 1918 address, which were created specifically for private addressing, so you can play as you wish on your home network.
10.0.0.0 – 10.255.255.255 (10.0.0.0/8) 172.16.0.0 – 172.31.255.255 (172.16.0.0/12) 192.168.0.0 – 192.168.255.255 (192.168.0.0/16)
These IP's are NAT (private) address space meaning they can talk outbound to any Internet host and in some cases inbound when certain TCP handshaking occurs that is defined to be opened by both sides. Such setups usually don't occur other than LAN breaches from an outside intruder who places a foreign/malicious machine on the LAN.
You can use any IP address on your LAN, do note that RFC 1627 describes why Network 10 is considered harmful. The goal of architects before the 1600's RFC's was that every node on the internet should be reachable and thus have public IP space. Firewalling is only ever needed if you fear for the safety of the network, which means a misdesign somewhere that isn't easily fixed.