Squares in a Square
Pretend the blue lines of the graph paper are the way the threads are woven (grain lines)
If I was going to make a block like this, and wanted all the grain lines to be perpendicular to each other, these are the triangles I would use.
I've found that the finished block presses out better when I cut the pieces like this.
Of course, if the center square has a motif that I want to fussy cut for a certain effect, I would do that! Or any of the other components, for that matter.
Yes, usually I would start with the center square cut on the bias.
I would also probably use the strip cutting method instead of cutting the squares diagonally.