I found that link to go over basics: https://www.heavym.net/choose-your-projector/

What you want to research is called (outdoor) "projection mapping", you need a lot of lumens (4k+), keystone correction and a 720p-capable projector for bigger numbers would be an overkill for such task. Pixelation is not a thing with projected images like it is with PC monitors, so at worst it may become blurry, but still okay, especially from afar. Default font sizes in presentation-making software are what you are aiming at, no small fonts and tiny details if possible.

Ideally, you'd also like to make it wirelessly controlled, so a small nettop box or an android phone with 4g/wifi and screen casting capabilities would make it possible. You'd usually only need an extension cord with two outlets for projector + image source device. You can test it at home before installation.

For software, don't seek specialized projection software since it's too complex for the task and usually paid, proprietary, exclusive to Mac/Win. You can try MiraCast as a popular option, or Chrome Remote Destop with a burner account. I think OBS with plugins is you best friend, with NDI or other way to stream media. You'd probably need to make a virtual lan network for them to work, but that's the last thing to worry about - and doable, after you test it all working over one wifi at home.

To break it into steps:

1. Make a sample image you want to project
2. Explore the area you want to put your hardware into, see if you can have a place to mount things and reach outlets via extension cords
3. Make a two-device setup with a spare PC monitor before buying a projector to test different ways to cast images from your source device, picking one
4. Measure by eye, if surface and angles, distances are right, choose the projector to fit them
5. Buy a projector and do your thing

P.S. If you want to do it without a secondary device, just by long cords, HDMI and DP can't do that and even if they can - it would be too expensive. You'd need SDI or RJ45 cables and converters from and to HDMI/DP (doubling as signal's power enchancers), as then you can transfer video signal over additional 50m+. But if you go into that territory, BEWARE for video tech is hillariously, mindblowingly picky about refresh rates, 1080p vs 1080i modes of coding signal and the weather on Mars at any particular time. I am a stupid man and skipped a lot of 101 courses alright but some of my setups using both pro tech or/and noname ripoffs needed a lot of trials and errors before making it produce any image at all. It is counterintuitive, but PC-PC screen casting over some network is usually more user-friendly and cheap than a field of pro video with decades of inventing gimmicks and inflating costs. It is less reliable, in theory, but it can can cover your needs right.

P.P.S.: For transfering video between devices, also check OBS forums for game streaming setups. I've seen many people using primary PC for gaming, then forwarding that screen into another PC that does the streaming part. Probably, there you'd encounter the best solution for your case.