In this scenario, you would not use a router. You would be using just a switch. A router is basically a 5 port switch (1 WAN 4 LAN) One of the ports (WAN) accepts the internet traffic. You have a DNS and DHCP server in the router as well. The 4 LAN ports are on a VLAN which connects to the DNS and DHCP server that will allow connection to the internet through the WAN port.
Many Home ISP companies also offer Business Class services which is the same service as their home lines but have a few perks. You get assigned IP addresses that are public to the internet.
However, most people do not have the proper hardware in a home scenario to protect each computer from attacks. Each device connected will be vulnerable to attacks.
Also, you are pretty much giving up your wireless access point since you would have to have static public IP addresses assigned.
All in all, unless you're planning on hosting several servers and other services, you are going down the wrong road. As Onxx said, if you have more information to what you're truly trying to accomplish, we may be able to point you in the right direction.