Let me clarify.
First off: I have a sheet of paper, 8 1/2" by 8 1/2". What are the optimal dimensions (<# of squares> by <# of squares>) of a checkerboard-patterned board that I could print on this sheet of paper?
Second: I'm creating a board in an image editor. The squares can be any dimensions (<# of pixels> by <# of pixels>). What are the optimal dimensions of the squares themselves, and what is the optimal dimensions of the board (<# of squares> by <# of squares>)
By optimal, I mean the most amount of squares that still looks aesthetically pleasing.
Also, I am open to different suggestions on what kind of "tiles" to use (i.e. squares or octagons or etc) and to what the dimensions are and sizes are. I merely chose checkerboard-style (square tiles) due to its ease of creation.