The routers themselves should also advertise which ISPs that they are compatible with. Otherwise, you are likely to find yourself frustrated at the fact that it does not work. You can find compatibility listings usually from various websites, but AT&T is unlikely to be very helpful in this department, as they want you to only use their devices.
To get Wi-Fi using a non-AT&T router, you will need to go through a list of the best routers for AT&T Uverse and FiOS to find the right one for you. But, having a gateway is not going to give you the wireless connectivity that you want or need.
If you have Uverse, your DSL provider will supply you with the gateway modem that brings the internet into your home.
That means for fiber, you will get the ONT box that supplies you with the internet. Any subscriber to AT&T, whether it is Uverse or fiber, will be set up with a residential gateway.