forget the word "modem", that's just for cable internet from coax to traditional ethernet. Fiber uses (same idea) an ONT to convert the optical signal to ethernet.
As for using your own gear, what you're looking to do is get the AT&T ONT box (which is also a router and wireless access point) into "IP passthrough mode". This should be very easy once you know the model of the ONT they supply to you. Now, plug your own router (I assume a standard wireless router) to have full control just like you had with Spectrum.
You might need to disable the ONT/Router's Wireless features if they don't turn off with the mode-change.
Note that the "first" device you plug in after switching it to IP-Passthrough is the device that will receive the public IP. So. I'd suggest you wire up as your final wiring will be before making that switch. Then just unplug your router from it and plug it back in for your router to receive a new IP (the public one).
Annoyingly, my AT&T ONT-Router was using the standard/common home IP range and was at http://192.168.1.254/. I say annoyingly because you might not be able to access it if you're behind your own router with the same 192.168.1.??? IP range. This is most easily fixed by changing yours to 192.168.0.??? (myself I like 10.0.0.??? == 10.0.0.0/24), but you can change the ONT-Router one if desired too.
Final Wiring for 99.9% of consumers using IP Passthrough mode: ONT >> Wireless Router >> home devices