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There are several screen size calculators online if you google it. You will find different recommendations from SMPTE and THX, for instance. The bottom line is, preferences vary, so you need to get some viewing experience yourself...
Here is some numbers according to THX for a 16:9 screen...for 13' distance you need a 101.4 wide or 116.3 diagonal screen; for 16' distance 124.8 wide or 143.2 diagonal

You can use your wall to project the movie to choose the right size, then buy or diy your screen :yes:
 
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