My recommendation is to go with a separate modem (connects to the cable and converts it to an Ethernet signal) and a separate router (takes that Ethernet signal, provides routing, WiFi, and other services).
Most likely they are DOCSIS 3 on your cable, so a DOCSIS 3 cable modem would work. ARRIS SB6183 or SB6141 would be a good choice. You can call them to verify those work.
Then you can pick a router. I like the Asus routers myself. Reliable and versatile. They have reasonable firewall services, and some other good security features. Most of them also support USB tethering to any Android phone or MiFi-type device so you can use wireless broadband as well as cable hookups.
Here's what ours is like mounted behind the main TV in our trailer. I have an SB6141 for cable internet, and an ADSL2+ modem if we have DSL service. I have a U301 from vzwmifi.com plugged into the router at this time.

If you have phone from them too, you'll want to ask what VoIP adapter they recommend. They should be able to give you the info to configure it.