Connecting to a cable modem, router or switch?

I recently switched from AT&T U-Verse to Charter.

My original setup with AT&T U-verse is their 2wire modem / router (4 Ethernet port out) to two Netgear wireless routers, one covers 1st floor) and another for the 2nd floor. My idea of having separate wireless routers for each floor instead of adding Wi-Fi range extender is not to oversaturate the Wi-Fi bandwidth. We have three kids, all live on 1st floor. I don't want their Wi-Fi toys (laptop, ipad, ps3, iphone, netflix tv etc) interfere with my media sharing process (2nd floor). In addition, each floor has multiple devices that can only be connected through Ethernet wire (voip phone, printer, av receiver etc).

Now, the cable modem Charter provided only has one Ethernet port out. If I want to connect it to my two existing wireless routers, do I need to purchase another wired router or gigabit switch? Which offer the best performance? Is the following network map correct?

Many thanks in advance!

Added (1). I don't need any feature such as VPN, Firewall and etc for this wired router or switch. Just a bare solution that connects both wireless router to the cable modem so multiple devices and go online simultaneously.

You may consult an IT support service. They can help you is solving your issue. They provide 24*7 help desk.

Well, before you go to all of that trouble, have you tried asking Charter for a cable modem with 2 or more LAN ports? Worse thing they can say is, "No."