I have a BenQ TH682ST projector. It is a full HD, short throw projector and is rather inexpensive. This is what I use to watch the vast majority of my content.
I can control this using the Harmony Hub so I should be able to control it using Alexa. The power off function required a double press of the power toggle button which I can replicate on the Harmony yet. Requires further work.
I run a Dell Micro PC attached to the projector which runs Plex and Sky Go but I’d also like to attach a satellite receiver to for FreeSat.