I recently purchased a BenQ W1080ST+ projector and I'm using my living room wall for projection. I don't plan to buy a screen because I don't want to invest so much to get rid of waves, and using a wall seems like an easy solution to this issue.
Well I see posts where people state how they don't want to go to too much trouble, but not nearly as many who go to such lengths to describe how poor their surface is to start out with.
If the Drywall itself is hung so that it has noticeable waves from uneven framing, there is nothing that sanding or even a skim coat of compound will take care of.
Personally...and this might sound a bit more rough than I normally express...I think your just trying to be a bit too lazy here. The available fixes are NOT expensive.....they simply require you to do SOMETHING to make things not just noticeably better, but exponentially better.
So read on and then let me either "have it", or take some good advice and wind up with a big picture you can be proud of.
Now, despite my wall texture being quite rough and the paint being some random matte stuff that the previous tenant painted I enjoy watching movies very much. I guess it means that my standards are not very high, and that I might be able to keep things simple when repainting. With this in mind I'd hope you can help me understand the following:
1. Can I get a reasonable result without the joint compound by just applying a layer of primer, sanding it and then painting the wall?
NO. All applying primer itself will only serve to change the wall color to white and prep the surface for a different paint. It will do nothing to hide the existing texture. Sanding after priming will mean you have to sand off the Primer to reach the root of your "Texture" problem. Of course that would still do nothing to solve your "Waves".
The most you could expect doing the least amount of work is to rid yourself of "some" of the noticeable bumpy texture by using a completely Flat Primer and Paint.
The "BEST" possible results would be from your taping off the desired screen area, taking a Medium Grit "Large" Sanding sponge, and sanding down the painted texture to a smooth as possible state. (elbow grease required). DO NOT sand to the point you see Drywall paper.
Then apply your Primer & Paint.
2. Is one layer of primer and one layer of paint sufficient or is it essential to do multiple layers?
If your Rolling (...and it is to be assumed you are...) you should / would have to apply at least 2 coats of Primer, and 2 coats of Paint
3. Do I need to finish with sanding, or just the paint?
That depends upon how well you can Roll apply the finish paint. In the least, wait a Day, shoot several different images onto the surface and inspect for Roller Marks. If any are present, sand the surface again and re-roll.
Basically, is there a way to invest 20% of the efforts of a multi-layer multi-material job and get 80% of the quality?
If only that were true, I'd have to answer far fewer questions.
Frankly speaking...and lower expectations considered....with all the issues your facing you should consider instead using a solid substrate. That is unless your Image Quality expectations are lower than your screen size expectations.
You knock one out of the park if your screen size falls to 98" diagonal or less, because there are smooth "Wave & Texture" free materials for under $20.00 you could simply roll on some Flat paint onto and you'd get past even that 80% improvement level.
Larger? There is Sintra or even BOC that would come into play..
Your biggest issue is that you obviously do not have any reference as to how extreme the difference would be if you did have a more acceptable surface. Because if you did....we would not be having this discussion about making do with a substandard surface.
OK...I have both feet firmly planted. Either give me your best shot...or take your best shot at going for something to be proud of.

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Post Note:
I see your answer to ftoast's reply, which somewhat mirrors my own suggestion to sand first then Prime & Paint. I really don't think any "test" is needed....just go ahead and do it.