In order to cover Windows, Android, Mac OS-X, and iOS, you'll need a two part solution.
As you've already discovered, Miracast is a wireless display standard. It is effectively HDMI-over-wireless. The Wi-Fi Alliance maintains a list of compatible products. Note that it can be called different things by different vendors; Samsung calls it "AllShare Cast" for instance.
Windows 8.1 and Windows 10 support Miracast. It depends on hardware support in the GPU, which modern Intel CPUs have integrated. Just be aware that having the right OS does not always mean the computer has the right hardware.
The same goes for Android - 4.2 and up have the software capability, but it's only useful if the phone or tablet has the hardware capability.
On the other side...
Apple has excluded themselves by Apple's choice, forcing their customers to purchase an AppleTV box as well. On sufficiently recent Intel-based Macs, part of the hardware to use Miracast/Wi-Di is theoretically there in the CPU, but there's no way to access it.
In order to get the same capability for Apple devices, you'll need to include an AppleTV in your setup. The AppleTV is small, so you can probably find some way to fasten it to the same mount as the projector and just leave it up there. It has Wi-Fi, so you don't need to supply anything but power.
In summary: Your projector will need Miracast-capability and an HDMI port for the Apple TV.