Non-Cox modem/router

A wifi extender will slow down your internet because it is half duplex. It can't send and receive at the same time. If you want to get around that, install a ethernet to the room with the weakest signal and install a access point(AP). If ethernet is not possible, and you have coaxial outlets in the room, look into MoCA. Either way, I suggest not getting a modem router combo but instead a stand alone modem and router. For the modem, the SB8200 is good but the Arris S33 is better if you want to future proof. As for the router, I like Asus but others here like Netgear. Do you have a price point in mind? Also, how big is your house?

I am using a Netgear RAXE 300 with good results. If you need more coverage, my suggestion would be to add a TP Link TL-WPA7510 KIT, which will use the ethernet port of your router to extend to the remote unit that I believe has an ethernet port on it, and dual band WiFi, that I have setup with the same ssid/wpa so it acts as a mesh network, with a backhaul to the router using powerline. If you have good power lines in the home, it's an excellent and fast option. If you DON'T have good power lines, then it will be SLOW. It works great for me, and my upstairs tv runs 4K without a hiccup, as does my downstairs tv. 

Power lines as in electrical sockets and the wires that connect them. YMMV when it comes to the quality and design of the electrical system in your house. It also depends what devices you have plugged into your sockets. Any kind of AC, heater system, or really anything that has a motor can backfeed noise into the line that play havoc on the powerline signal. I say it goes Ethernet > MoCA > Mesh > Powerline > Weak Wifi in order of performance. If you can run ethernet into the room with weak signal I think that would be your best bet.