Suggestions for new modem and router

hello internet, once again i must ask for your mystical knowledge for finding a new modem and router. here are some of my requirements and info that you might need to know

  •  the modem has to be DOCSIS 3.0
  • My ISP is Mediacom and i am getting 100Mbps 
  • we have a pretty big house so it has to cover quite a bit
  • i would prefer it to have external antennas just so i can change the antennas if i feel like doing so
  • none of the devices that connect to the net have AC capabilities
  • it has to be under $200 total


I don't have personal experience with this router so I'm not exactly sure its effective range but I do have this modem and it's actually quite good.



If you've got an old computer lying around, make a pfsense box, get a cheapo switch with a few gigabit ports and a unifi ap?

^^^^ this^^^^

the only problem i see with that router is it is not dual band =\