all a router does is assign IP addresses. the most common routers (linksys and others) are actually routers with built in switches basically the definitions look like this

Router: assigns IP to computers that connect to it, and provides a "front" for a network, hiding all computers behind it on a single IP on the WAN (wide area network, i.e. your neighborhood, or the whole internet)

Hub: Takes packets and rebroadcasts them to every computer connected to it. All computers under a hub will "share" the bandwith because only one can "talk" at a time.

Switch: is a smart hub. it looks at where packets are trying to go, and makes a number of connections very rapidly, segmenting the network and making the neccesary connections on its own. this allows multiple connections to be active at the same time, with everything operating at full speed (more or less).

The routers you're looking at buying are routers with built in switches. if you're doing a LAN and you want internet access, the way to you want to do it is thusly: cable modem connected to WAN port on router, computers connected to router's built in switch. if you have more computers than that, buy a switch (a hub will work too, but a switch is more better-er), and plug the uplink port on the switch into one of the router ports, and then the other computers into the switch. if you run out of ports again, the same applies, another switch into one of the first switch's ports will add more ports to your network. This daisy chain can be continued quite a ways, up to, I believe, 254 computers. Basically, anything that can "connect" to the router, either through its built in switch, or a daisy-chained switch or hub, will be assigned an IP and be able to access the internet through the router.