There is no standard poster size. 16" x 20" is a standard (large) picture frame size. You could always go larger. I would suggest you ask the client what size were they thinking of. Once you have the size, then you can determine the size of the squares and rectangles.
Then you would need to determine if you are going to put a border around it. That would add to the final size.
Based on your photo, it is 12 squares wide x 16 squares long. If you made each square 2" x 2", the size before a border would be 24" x 32" (calculation: 2" x the number of squares) without a border.