Jim:
Frontier will provide two devices:
1. An Optical Network Terminal (ONT) and
2. a router (typically an Arris model).
Both devices need a standard AC outlet nearby. They have independent power, and do not provide power to other devices via Coax or Ethernet. WRT length of run to the router, I assume it's highly dependent on the tech and how far behind he is on his site installs.
Both devices have Ethernet as well as MoCA (i.e., coax) ports. The coax port *only* matters if you need Frontier video service, and they use standard RG-6, not the thinner RG-59. Coax wiring is not needed if all you want is the
FiOS Internet service. I'm going to assume you only want the Internet service.
Important: Specify, at the time you order, that you want the ONT Ethernet port live and connected at the time of installation. If you order online and there is no place for that specific instruction, tell the tech when they call to confirm the installation appointment date.
First they install the ONT on your property - they want to install it on an inside wall near AC power: A garage wall is common.
Then they want to connect that ONT to their Arris router. Assuming you explicitly asked for a live Ethernet connection, they connect with Cat 5e or better Ethernet cable. If you order 100/100, you really want Cat 5e or better.
If you get 100/100 or faster service, they will bring an Arris box to match. If you get something less (i.e., less than 75/75, they will bring a less capable router, necessitating another (not free) installation visit by the tech if you choose to upgrade later. Moral of the story: get 100/100 or faster service from the get go.
The Arris router is *not* a requirement. You can use your own router instead (I do) and place the Arris in storage. Important: if you ordered 100/100 or better service and want to use your own router, make sure the repurposed router has GigE ports, not cheapie "Fast" Ehernet (limited to 100Mbps max).