Projector position is pretty much entirely determined by screen size. So, you have to start with a known screen size.
Let's say you have a 120" diagonal screen.
Then you mosey on over to Projector Central and their calculator...
With a 120" diagonal, the lens to screen distance may be anywhere between 11'7" to 18'10". Anywhere in that range is fine, but if you want to maximize light output, you want to be on the closer end of that range. Call it about 13' lens to screen.
The lens must also be about even with the top edge of the screen, so your projector mount must allow that to be the case.
Then, everything else comes into play.
Does that location work in your room?
Are you happy with the height and location?
Do you need that many lumens on screen?
There is a bit of flexibility with the height as the projector has a tiny bit of lens shift, but not much. A few inches.
Fan noise is really not a major factor. Placing a projector directly overhead is often a good spot because the fans blow out the sides, instead of straight down, which lowers the noise from them.