For DSL, there are DSL modems and combination DSL modem/routers. With a DSL modem any standard router will work.
For Cable, you will need a cable modem and a standard router.
For WiFi use, you may need a WiFi adapter for the PC (if it isn't WiFi equipped).
And as before if you are using LAN, then you would need the ethernet cables to connect the modem to the router and for the connection of the router to the PC.