Most of them are using commodity hardware from Mikrotik, Teltonika and Ubiquiti. Basic setup for a personal node is just an antenna + router. Then they usually have the concept of "supernodes" who are responsible for hooking up multiple personal nodes, and have uni-directional antennas + multiple ones + bigger routers to facilitate the routing.
I'm not sure you'll be able to put together a supernode with decent range for under $100 though, think the cost would be more than that, but I would be happy to be proven wrong.
In terms of firmware, I've almost exclusively seen OpenWRT being used (and the rest running default Mikrotik/Ubiquiti firmware), with various self-made patches done to it before installing it on the hardware.