Welcome to the binding decisions group. There are many different techniques for binding. Take some time to discover your perfect way.
Binding 101 has been a process for me but it does get easier. I suggest some practice samples first on some blocks. Mark right on the block the cut binding width and the stitch settings.
For 2 1/2 inch binding, I use a 3/8 inch seam allowance on the first side stitch down.
For 2 1/4 inch binding, I use a 1/4 inch seam allowance on the first side stitch down.
Typically, I stitch the binding to the back of the quilt and bring to the front. I can see where I'm stitching the binding edges and get a fairly straight line.
I don't press binding in half. The crease is in the wrong place for the final fold over when you look at it lengthwise.