I also used to press my binding in half before applying it, but since I read on the board about not doing so, and tried it, I am totally devoted to the not pressing. I do finger press the joinings of the binding, or use my wooden stylus, as I go along. I do not use bias binding as I find it both too wasteful of fabric and not better in appearance than the WOF way I cut it. With bias, you are still showing a seam on each side, and mine never seem to be that bulky.
I do stay stitch the edge of my quilt to the backing around the edges before I trim the quilt. It's extra work but helps me keep those edges of all layers together.
I cut my binding just a little wider than most, at 2.75". I do all machine binding and that little bit extra helps me keep the seams neat. I stitch the binding to the back first then fold it to the front and stitch it down. My stitching foot has a little mark just where I need to line it up for nice even stitching on the front.