I’ve done it both ways. In either case, you at least need an access point that’s capable of handling the number of devices you plan to have on the network, but it’s good to have a dedicated AP with a separate SSID on a different channel.
Some people even segment networks with VLANs to isolate devices, so that’s a consideration too.
That design is asking a lot from wood. You could do it with metal, but wood needs bracing.
Have you considered adding metal L brackets?