What kind of router do I need?

D-Link AC1200 Wi-Fi Router (DIR-842) 

you can try any of them

Asus ROG Rapture GT-AC5300

Netgear Nighthawk X10 AD7200 Smart WiFi Router (R9000) 

D-Link AC1200 Wi-Fi Router (DIR-842) 

You need an approved device.  The first thing is if you want a integrated modem/router or separate.  There are good things for either:

integrated: Easier to debug, less cabling, less power outlets, when it dies, everything is dead

separate: you can upgrade (wireless or routers) at will, replace modem without replacing router

Personally, I think the wifi on their routers (which are Arris) is crap.  When I had one, I had to install 2 APs to get wifi coverage.

I've had the same modem (Surfboard) for about 10 years.  I've had at least 2 dead routers in that time, if not more.

So I prefer separate, but I have lots of things behind it so I know how to debug it.  But if you just want wifi and wired and not much more, then you might just want a integrated.

When we moved, I got a leased box.  That way, I knew it worked and it was preprovisioned.  But then almost immediately I used my own gear and returned the Xfinity stuff. Now let me say, at the time I could only provision during business hours.  Perhaps it has changed.  But if you don't want frustration, I would lease for a month and THEN switch.  That way, either the old gear or new gear will work.

Technically there are two pieces of equipment you need to connect to Xfinity.

1. Cable modem.  Ideally the cable modem should be DOCSIS 3.1 compatible, however a DCOSIS 3.0 compatible cable modem will work with Xfinity.

2. Router.

Sometimes both devices are integrated together, a combo device is what you would get from Xfinity.

For the cable modem (or combo device) you need to get one that is approved by Xfinity for compatibility with their network.  https://www.xfinity.com/support/articles/list-of-a...

The cable modem converts the analog "cable" signal over to Ethernet.

The router allows you connect more than 1 device to the Internet at a time. 

The router doesn't need anything special with respect to compatibility with Xfinity.  

What you should consider with a router is how much space do you need the Wi-Fi to cover?  Wi-Fi works like a low power radio transmitter/receiver.  If your home is large or you have coverage issues you might consider getting a "mesh router".  A mesh router allows you to easily connect extra Wi-Fi access points to expand your Wi-Fi coverage.  If your home is small than most any router will work for you.

Ask Xfinity. They have no reason to withhold that information from you.

You will need to check with xfinity from a list of their approved modems

https://www.xfinity.com/support/articles/list-of-a...

Very smart! Pick up a mid-priced wifi router from Target. Mine's a Netgear. It was about $60.00.