For a kick off you have the choice of either wired or wireless router. A wired router as the name suggests means that your laptop would be physically connected to the router by a cable. Wireless as you can imagine means the connect takes place by the router sending and receiving information by transmitting it through the air, i.e. a bit like a radio. For the wirelss option you'll also need a wireless capability on your laptop, which may well be build in or could be added by buying a wireless card for it.
Next, depending on your broadband service will determine whether you want/need to get a router that had a modem built in or a router that will go between your exising modem and PC(s).