Using a different router

We have the att fiber 1000 speed and using two airties extenders. We just had the modem and optical terminal network replaced due to constant disconnecting. My kids play online games and are saying they Are getting a lot of lagging while playing, even when they have the Ethernet connected from the airtie to their PlayStation. They each have an extender in their rooms.  I have read about using our own router. Im looking into the netgear nighthawk. How would I connect that?  Do I still use the att gateway?  Would using a better router give better signals? Thanks