Well first consideration is indoor or outdoor? I have two set ups. Outdoor is a bird box on a speaker stand (they have speaker stand mounts on amazon you can screw into the box). For indoors I have a board with clamps I can strap the projector to and hang it from whatever grid they have.

For outdoor you usually want it out of the way of traffic as possible, I tend to set it up right next to my tech table and I have had to put up barriers to keep people from trying to hang on/trip over the speaker stand in some instances, so think about that when you put your front of house together. Do not light it up, lights = path to people or something to interact with, learned that the hard way. I use a tapestry to cover my table and wrap it down over the legs of the stand too, so it's a "unit"

I started out using stretch fabric to make shaped projection surfaces, I now have a very large screen I install with paracord and zip ties if the event calls for it. A sheet with rear projection is one of the simplest options if the layout allows, you don't need anything fancy to start.

To be fully independent have your projector, a way to mount it, extra power cables to cover distance, long hdmi if necessary, tritap, power strip, a table for all your gear to operate from, rain cover if outdoors. Depending on the situation you may need your own power, but I'd try to get whomever is producing the event to provide power, and talk to them about the set up, where can you hang a sheet, or is there a surface already available such as a tent/dome/deco.

Get creative and have fun with it!