How much would a AT&T Wi-Fi would cost monthly?

If you have AT&T DSL or Uverse, Wi-Fi does not cost anything extra, other than to buy a wireless router if you have a simple DSL modem/router instead of gateway (wireless/router/modem). There's no extra monthly fee or anything for Wi-Fi.

If you are thinking of something like a mobile Wi-Fi hotspot (that uses mobile data for Internet access), that is not really optimum for gaming. It works fine for something like minecraft, but ping would be high and lag would likely be noticeable in quicker games like first person shooters. A LOT. Youll have to get the estimate It varies from area to area. You need to talk to your local service. You never get the full speed you pay for though.

A LOT.

Youll have to get the estimate

It varies from area to area. You need to talk to your local service. You never get the full speed you pay for though.