If you're planning to use coaxial cable for networking, you can either implement a technology from the 80's (Thinnet) or MoCA.
Thinnet involves NICs and routers with BNC T-connectors and cable terminators, but nobody makes that stuff anymore. I've read the technology for MoCA is getting better but...in my opinion...you're still trying to improve the buggy whip.
If your current WiFi range is good, stick with it. If not and you're renting a Cox router, you may be limited to only Cox MoCA adapters. If you're not renting, you can read reviews about other network extenders or mesh technologies.
Running Cat cable is difficult but not impossible. You just need to find the path of least resistance (drilling & cutting) between your downstairs router and a strategic spot for an upstairs router. This will take thoughtful and thorough planning.
