Considering the size of coverage you want to have, you’re better off with the cascading router setup. Since the computer can access the internet wired to the 250ft cable, this should work.
There are two ways to cascade a router:
LAN-LAN : Router 1 (numbered port) <> (numbered port) router 2
LAN-WAN : Router 1 (numbered port) <> (internet port) router 2
If you’re doing LAN-LAN, the IP should be the same as the main router except the last octet. If router 1 has a gateway of 192.168.1.1 then the cascaded router should be set up with 192.168.1.2. The DHCP server needs to be disabled with router 2.
If you’re doing LAN-WAN, you’ll just have to change the 3rd octet of the Gateway so there won’t be a conflict. If router 1 has 192.168.1.1, then router 2 needs to have 192.168.2.1 gateway.
My setup is LAN-LAN. I chose that so I can easily transfer files to computers connected to either router. It’s easier to network devices if they have the same range of IP address.