The official tech support does not do home network planning. For questions like this, you need to ask them here.
Like I said, if you can repurpose the telephone CAT5e's into Ethernets, that's the cheapest way to go. You can use any router you want and can have the router upstairs.
If not, you can either buy a non-VZ router and a pair (2) of MoCA adapters, OR a VZ router with a single (1) MoCA adapter. The MoCA adapter you linked is overpriced. goCoax is cheaper even comes with 2.5GbE ports.
The Verizon G3100 and E3200 can utilize the existing coaxial cable infrastructure. The 3200 has two Ethernet jacks on the back which can be used to support a computer and a switch (to allow more devices to be connected to the network).
I would like to thank everyone for taking the time to post your comments and opinions related to this topic. This topic has been thoroughly discussed and will now be closed. Please feel free to open a new thread for further discussion. Thank you.