For the access point, I would also go with UniFi. I am currently running the AC-Lite. It is sufficient for me at the moment, but other models are of course even better.
How many POE devices are there in the entire network? If there are only 2 devices, I would use the supplied injectors. For more POE devices, I would use a POE-capable switch with just over the number of required ports and a regular switch for the rest. I like the devices from Zyxel’s Grundstück-1900 series, but many other manufacturers also have good devices.