Since you are asking about design and haven't actually started construction, I'm gonna move this to Home Theater Design.
There are some formulas available for room size that might help you decide on the size, if you have the freedom to build any size you so desire. A few that I've seen posted here:
Height x Width x Length
1 x 1.28 x 1.54
1 x 1.26 x 1.59
1 x 1.4 x 1.9
1 x 1.6 x 2.33
10H X 16W X 23.3D would be pretty close to what you are considering, which is using the 1 x 1.6 x 2.33 formula.
The
Room Mode Calculator might be of some help too.
This
Viewing Distance Calculator may also be useful.
Any particular reason why you would use a rear projection instead of a front projection system?