There are compromises all round when it comes to screen size, but here are some guidelines…
There is no fixed rule for this, but some folk suggest that the height of the screen should be 1/6 of the distance from the screen to the furthest away viewer. If you try this, you might find that it gives you a BIG screen, and you can probably go smaller. If aesthetics are important and you can push the size of the text onscreen up and have more pages per song, then you might get off with a smaller screen, which would help your brightness levels a lot. (Remember that the same lumens are spread over a larger screen area, so a larger screen will ALWAYS be dimmer than a smaller one, with the same projector).
To give you some guidance, for a smaller audience, say up to 300 people, an 8ft x 6ft screen is often fine. If you are pushing up to 500-1000 you might want to go to 10ft x 7.5ft, and if you have a huge barn with 1000+ people then you are into the realms of bigger screens still. Remember that there are disadvantages to a larger screen too (see above) so don’t go bigger unless you really have to.
Once you know the screen size, and the screen diagonal size in particular (150in for a 10×7.5 and 120in for an 8×6), then all the user manuals for projectors will tell you what distance the projector needs to be from the screen to fill that size of screen. It varies from projector to projector depending on the lens. To give you an example, our Hitachi CP-X995 (4500 lumens) projectors need a minimum of 5.5m behind a 10×7.5 screen or 4.4m behind an 8×6 screen. Other projectors may vary.
Most smaller projectors have quite wide angle lenses as they are designed for sitting on a conference room table, whereas larger ones are often assumed to be ceiling mount and have longer throw lenses. You CAN buy special wide angle lenses for most mid-range projectors, but they are VERY expensive and you want to avoid having to do this and put all your money into a brighter projector instead.