Netgear AC2300 R7000P Question

[SheevaBlaster]

I'm getting the AC2300 Nighthawk tomorrow and I'm kind of confused where I'll be plugging the ethernet cable that comes with it.

 

So I understand I'm plugging the yellow cable that comes with it into the port that's clearly labeled "internet" on the nighthawk, but where do I plug the other end to? Do I plug it into the LAN or WAN port on my Verizon Modem/Router? I have the FIOS-G1100. After getting everything set up, I should proceed to transfer my wired cables from the LAN ports in the G1100 and plug them into the LAN ports of the Nighthawk correct? Does it matter? just Genuinely curious. 

 

Also, should this be a noticeable upgrade? I'm looking to upgrade my wifi mainly because I get no signal on one side of the house and downstairs. I've considered mesh systems along with moving the router itself, but I'm lazy and I'm hoping this Nighthawk should remedy the range issue. Based on my preliminary research, it seems that the G1100 has a range of 325 sq. ft. while the AC2300 is rated for 2,000 sq. ft. so I'm hoping increasing the range 6 times should be more than enough to maintain steady signals for my wireless devices found on the other side of the house. I know there's numerous factors that go into this such as what my house is made of and other disrupting factors, I guess what I'm asking for is for personal experiences with the AC2300.

 

Any insight would be much appreciated!