If it comes in via a coax port it is likely going to need a cable modem. Even though technically there are likely a number of modems that will work you are going to be restricted to the ones the ISP has on their list of supported devices. Since the ISP actually controls the modem they do not want a lot of different brands of devices they must know how to support.
Almost all routers with gigabit lan and wan ports can support a gigabit internet connection. That is only via ethernet though. There is no wifi that can come even close to gigabit speeds. The router though is only 1/2 the wifi connection. The wifi radios in your end device likely will limit you well before the router does.