the vertical image shift would depend on what projector you get. I feel like i'm over generalizing, but most home theater projectors need to be placed somewhere between the top and bottom of the screen. Many data projectors come with more of an offset to allow them to be mounted higher (or lower) than the screen. The projector in my classroom is mounted like 12' but projects onto my white board at about 8'(top)
there are a few things you need to make sure are all compatible to make this work
-how far the projector is from the screen. the farther the throw distance, the larger the image will be. most projectors have at least a little zoom give you a size range at any given throw distance
-provides a range of image sizes at a given throw distance. For example, at my current position, my projector can zoom anywhere from about 140" to 85"
"IMAGE OFFSET' (in quotes because i'm not sure what the proper name for this is)
-most projectors are designed to be place near the top or bottom edge of the screen, not directly in the middle. the amount the image is shifted up/down from center is the offset. typically there is no horizontal offset, only vertical
-allows you to shift the picture up/down or left/right (change the offset). cheaper projectors have pretty limited, sometimes no lens shift at all. this makes them a lot more of a challenge to mount perfectly
all of the above things can be different in different projectors. So when you're looking at models, be sure to check these things to ensure you can project the right sized image to the right location from your desired throw distance.
start off my figuring out where you'd like your projector to be. try to pick a spot directly in the middle of your screen location (horizontally). When you know what height and throw distance that will be, then you can start figuring out how big you'd like the image, and people can start recommending projectors that can provide that. Or alternatively, if you're flexible with the projector mounting, pick a screen size, research some projectors, then you can figure out where those projectors need to be mounted in order to project the desired image
i think if you want to get more specific help, you'll need to provide info such as a budget, what content you intend to watch, details about the room like color and whether or not there will be any light