Well, I doubt you'll find a modem/router combo for $100 or less..

I'd got the separate modem + router route.. for the modem either the Netgear CM500-1AZNAS, or the Arris SB6183

and for the router, something like a D-Link DIR 878.. this is an AC 1200 class router that supports MU-MIMO which is important if you have multiple WiFi devices in use..

Now I am not all that familiar with FIOS but I do believe that you can use your own router so whatever router you get, so long as it supports gigabit ethernet, you can use it with whatever service you end up with after your move.