You can do this without buying a Router but I HIGHLY suggest that you do it - if for the built-in firewall if nothing else. Heck, get a wireless router for $40 and you'll be WiFi ready and sharing with your wired computers.
You a router that does NAT - Network Address Translation - which I am unaware of one that doesn't do that. The Router will take the IP address from the ISP and use other IP addresses for the computers inside the Router - most will handle up to 254 so you should be good to go unless you've got a really big family. Set each home computer to use DHCP - Dynamic Host Configuration Protocol - from inside the Network applet (control panel/network). When they boot up they'll ask the Router for an IP address.
There is a software solution built-into to XP called the Microsoft Internet Connection Sharing - to a start/help and support/search for that and it will walk you though.