Router Mesh Network (Wired & Wireless)?

I am currently working on a project that requires me to have a few (for now, let's limit it to three routers), send data among themselves and one router to be the gateway to the internet. The routers will be connected over ethernet (Do I require a switch for the three routers to be interconnected?) cable, but as a failsafe, should also communicate over WiFi in case a cable snaps (the project is to be deployed in an environment with frequent mechanical wear). I was thinking of keeping one router in the access point configuration and the rest in client mode. Does this topology make sense or are there better ways of going about it?

How can I go about achieving this using OpenWRT? Is it advisable that I get Raspberry Pi(s) or other Single-Board Computerin addition to the routers? Forgive my lack of knowledge in the networking domain, but I'm keen to learn. Any and all advice is helpful. Thanks all!