My home office local network isn't anything special; many others have a similar setup. I have cable internet service, a wireless router, Lingo VOIP telephone service, and several computers. Here's the layout -
The cable modem, on it's own, creates an Internet connection, with the IP assigned dynamically by the ISP.
My domain name, datix.us, is associated to the external IP address through godaddy.com's DNS service. Fortunately, the dynamically assigned address hardly ever changes, because godaddy makes updating this info very difficult.
The Lingo ATA (analog telephone adapter) is connected to the inner side of the router and magically is able to function on the cable internet connection. Lingo recommends placing it between the cable modem and the router, but this arrangement works fine. All the household phones are connected in parallel to the single phone jack on the ATA.
The router performs NAT (Network Address Translation) so that packets from internal machines are converted to the external IP address. It contains firewall rules so that packets arriving from the internet are blocked except for selected kinds, which are passed through to datium, the main server. Only ssh, imap, smtp and http packets are allowed. These allow me to access the main server from outside, read my mail, send and receive mail, and operate an apache web service.
DNS and DHCP services are disabled in the router and provided instead by the main server, datium. The Linux programs are much more versatile. Local IP's are assigned both dynamically and statically, based on the MAC address of the requesting machine. Reverse lookup data is maintained correctly, so all local machines can access one another by name or by IP.
I have no dedicated Windows machines, but do run Windows on rare occasions inside VMware virtual machines. These are not shown in the diagram, but do show up on the LAN as distinct machines when they are operating. All the Linux machines run samba to make their filesystems and printers available to these virtual Windows machines.