First make sure the Broadband (DSL/Cable/???) you get has an Ethernet connection to your system. If it only has a USB interface, you have to use Internet Connection software on one computer to share it. Then create a network to the other systems which may require a hub (which costs almost as much as a router.)
With an Ethernet interface from the modem to the system, you have a mini network already. The router between the two creates a real Network. The router can then share the connection between any systems connected and also act as an inbound firewall.
You can get home routers at Best Buy, CompUSA, Office MAX, etc. Almost any place that sells computers. Check the Sunday AD's. Most are under $50. Wifi enabled routers are a little more expensive but worth the investment if you have a laptop you want to connect into the home network.
The only problems come in if you are trying to run a server, or expect to play on-line games from more than one system at a time.
You also have to understand what sort of broadband connection you have first. Most DSL ISP's use PPPoE which requires a user login and password, often done with a program running on the system. This information has to be put into the router for it to handle any login. Also AOL can be a problem if they are your ISP. Avoid their setup if possible. There are ways around their method of home networking which requires each system to have its own Screen Name login and password. (Just create a special one for the router only.)