Att calls pretty much all their internet offerings U-verse from crap dsl to their gigafiber.
Which router greatly depends on which service you are getting. Even after that att has a lot of their systems rigged so you can not replace their router. Not 100% sure why but in some cases it is related to their cable tv boxes being dependent on their router.
You will have to investigate which plans and what options you have. In general the routers provided by ISP will run at the speeds they have committed to in their contracts so a different router will not be faster. Some have poor wireless coverage but most are similar in performance to any other router you will buy. Mostly you would want to replace the router for some feature...