I have a cisco epc3825 cablemodem that provides internet to a number of PC's via Wifi. I'd like to add Linux PC on the LAN to monitor traffic usage on all PC's on the same LAN. Is this possible? Would this require some sort of man-in-the-middle -scheme to work?
Yes, this is possible and rather easy to set up. If you have access to the LAN, you can use a passive sniffer such as Wireshark or tcpdump to monitor all of the traffic on the network. There are tons of tutorials online for how to set up Wireshark to capture network traffic. Here is a link to the official documentation: Wireshark User's Guide.
However, for any traffic that is encrypted (with SSL/TLS, SSH, etc) you will be able to capture the packets, but won't be able to read the data. In that case, you would have to resort to some sort of MITM attack using a tool like sslsniff/sslstrip. For an explanation of how this works, check out this video: Defeating SSL using sslstrip.