A:
You always need a modem device to bring in you internet signal...either by cable, DSL (telephone line), or satellite.
A router is what will create a wifi signal for your internet....that means all you wireless devices can connect to this signal without having to directly connect them by ethernet line to your modem.
All in One gateway Devices work both as your router and modem, if you like to hassle with less wires and equipment, list these type of devices under consideration.