I think there are 2 different things here? A "router" is just the device that connects to the "modem". The router then has the extra ports and WiFi that you connect to from your devices (computer, phone, tablet, etc)
The modem is what connects your home to the internet from your provider.
I'm with Xfinity/Comcast and they can supply you with their modem/router combo as a single unit and charge you a monthly rental.
I bought my own modem (Arris) that would work with them (after you spent about 30 minutes on the phone with Xfinity tech support to activate it) and then just got a Linksys router/wifi to connect to the modem and then to all my devices. It's also a 'firewall' as such too.
I already pay way too much for Xfinity/Comcast cable/internet service... I sure as heck was not going to pay rent on their internet hardware... Sure, I have to rent their TV stuff.... But, there you go! ha, ha...
Good luck! Mitch