click here for an explanation of what a router is/does.
If you buy an adsl modem that connects via ethernet, you can connect it to just about any router. If you buy one that connects via USB, there are only a couple of routers that you can connect it to.
If you buy a PCI modem, you cannot connect it to a router at all.
If you buy a combined ADSL modem & router, you have the greatest flexibilty.
If you do not intend to set up a home network, forget about routers - you don't need one.