Good advice so far. This is an interesting question because I was thinking about this as I was driving into work this morning. I've already had my projector set up for many years. Another forum user was asking similar questions.
There's a whole bunch of parameters that interact with each other. So if you change one, it affects the other. For instance if you change your viewing distance, that may affect the size of the screen. But in my opinion, it goes something like this:
1. Since you have a room, find a wall and find your seating area. Now measure the viewing distance from your eyes to where the screen is going to be.
2. Now that you have the viewing distance, an important parameter is called the field of view. SMPTE and THX both have recommendations. See this link for a field of view calculator. THX recommends about 36° to 40°. For my room I chose 40°. You can try this calculator to punch in some numbers such as your viewing distance, and then you can select a diagonal of a 16x9 screen and you could play around with the diagonal value in order to get a 40 degree viewing angle.
Viewing Distance Calculator
myhometheater.homestead.com
3. Great so far. You know how large your screen is. And you have the viewing distance. The next critical factor is brightness. SMPTE has a recommendation for movie theater brightness. It is measured in foot lambers. The standard is 16-ft Lambert's. You get to foot Lambert's by taking the lumen output of your projector and dividing it by the square feet of your projected image on the screen. Using the diagonal screen size from step number two, you can compute your square footage of your screen. As an example, my screen is 135 in 16x9. You can try this screen calculator, put in the diagonal, and then click the calculate button to compute the width and height. If you're using inches, multiply the height and the width and divide by 144. My screen, I get 54.1 sq ft.
This calculator helps converting the size and dimension of a screen (in cm and inches) into each other.
screen-size.info
So in my case, I get 54.1 ft * 16 ft Lambert's = 865 lumens
4. Now you have to account for aging of a bulb, which generally ages 50% as you know. So you may need a projector, if you were in my case, 1700 lumens just to have the bulb in by 50% so you can get your 865 lumens that you need for 16 ft Lambert's. Unless you go laser projector which is a different ball game because you don't get the dimming that you do with the bulb.
5. There's a whole bunch of parameters that affect the calculations that we did above. It's just the first run through in order to size your screen based on your viewing distance. The calculations are pretty standard for 16x9 screen.
I hope that was helpful.
-T