Everyone who has broadband should already have a modem. So im assuming you have DSL/Cable?
You need to connect your modem to the router and the router to the 360. Since you have a wireless router im guessing you have a wireless adapter on your 360? If so thats all you need to do to set it up. If if you dont have the wireless adapter you still need to connect your 360 to the router.
You also do not need a PC to connect to live, just a modem, router, or both.