I cut my binding at 2-1/4 for 1/4 inch binding but find it impossible to get a straight line of stitching from the front to catch all of the back binding edge. I have tried pins, clips and dots of glue but I am never happy. If you use a fancy stitch it works better but not perfect.
If I want to machine stitch my bindings, I always use Charisma's Quick Machine Binding with flange tutorial here on QB. She gives the measurements for finished 1/4 inch binding with 1/8 inch flange that you stitch down from the front. If you match your thread to the backing it matches right in. If you wanted the binding to finish at 1/2 inch with a flange, you would change the measurements of your binding strips. I think it would work out to be a 2 inch strip for the flange colour and a 1-3/4 inch strip for the binding and they are sewn together and folded. Try a sample and see how you like it.