Kinston: First, let's get the correct units. 1200 mbps is extremely slow. You meant 1200 Mbps. M = Mega, while m = milli which is a billion times smaller.
If you are gaming, then you really ought to be using Ethernet connected devices. WiFi can be very erratic, with interference from other devices on the WiFi network and interference from other nearby WiFi networks.
Before wasting money on an 802.11ac router, check that the devices you want to use with it support operation on 5 GHz. Many devices work only on 2.4 GHz.
Providing the modem has an Ethernet output and the router has an Ethernet WAN/internet port, then you should be able to use an 802.11ac router with your 500 Mbps ISP connection. Although you cannot exceed the speed of the ISP connection for transfers to/from the Internet, you may get higher speeds for internal networking, especially is the router has Gigabit Ethernet ports and you have a file or media server with a Gigabit port connected to the router.
Finally, since WiFi can pass only one packet at a time across all connected devices and there are frequently data packets going in one direction and acknowledgements going in the opposite direction, WiFi speeds are frequently capable of sustained speeds of only 50% or less of the peak speed. Depending on what is being transferred, 1200 Mbps WiFi might only give you 400 to 500 Mbps shared between all devices on the WiFi network. In contrast, Ethernet is a dedicated connection to the router and supports packets going in both directions, so a Gigabit Ethernet could give you 850 Mbps or more to the router and out to another Ethernet connected device. The ISP connection will still limit Internet connection to 500 Mbps.
I hope this helps.
Routers can work with any modem and speed. Modem speed and internal network speed are NOT related.
For example, I have 200 Mbps down and 20 up. My internal network is Gigabit for the Ethernet connections and various for the WiFi. (1300 Mbps) While the WiFi max CAN Be higher, in practice, I never see more than about 750 Mbps. All this means is that I can transfer files at speeds in excess of 100 Megabytes per second should the devices be able to take it at that speed (other than two computers with SSD's, none can handle that kind of speed) My downloads are limited by the incoming connection which is a fifth of the Ethernet speed. Microsoft once sent me files at 17 MBps but that is very rare. My download speed has nothing to do with my local LAN speed.
yes… your internet is ALWAYS the slowest point in a connection. it does not matter….
if you can do 12 math problems per min and your teacher gives you 5 per min will there be a problem? no because you can work faster than you currently are
Yes, as long as the modem has and ethernet port to connect the router to, they can work together. If you have two devices on the router, they will be able to communicate at up to 1200 mb, but any connection out to the internet will top out at 500.