what type of Cables are needed for router

For a typical broadband router, you need a cat5 cable to connect the router WAN port to the DSL modem, and you need cat5 cables to connect each computer to a router LAN port.

For a router/modem combo, you need cat5 cables to connect each computer to a router LAN port, and you need a telephone cable to connect the modem to the phone line. Some people recommend twisted pair for the telephone cable. If the phone cable is short enough that won't matter.

Any ethernet cables would be standard CAT5 or better 'patch' cables unless doing something unusual (like connecting 2 routers LAN2LAN which might require a 'crossover' cable).

As far as modem to phone line, I have not had any trouble using any phone cord (even 25' flat modular extension cord), although, twisted pair is best (round cord).