Best would be newest AC router, like Asus AC66U, but few devices has AC capabilities. They are backward compatible and can run N. For N, look at 450mbps ones. I hear good things about the Asus N66U.
As to why you old setup only allows X to have Internet access, you ISP only provides X IP address. If they provide 1 IP, only one device can connect, 2 IP = 2 devices and so on. If you want more devices to work, you need to use a router, not a switch, since they can take 1 IP and provide a hundred virtual internal IPs.
Most of recent routers are good at handling gaming data and/or have included settings for popular services, Xbox Live, Steam and etc. this, it shouldn't be an issue.
AC capabillities? And what do you mean with run N?
Thanks for the advice btw. That Asus AC66U is a bit too expensive for me atm. But I'll think about it. My ISP is supposed to give me a wireless modem, but they promised that years ago and still haven't for some reason.
Also if I get a new router do I connect my modem to my router or just just replace my modem with the new router?