This is a great video that I recently watched.
https://www.youtube.com/watch?v=dQgjp4Upt8w
There is a "sweet spot" for that first stitch down. If you are using 2 1/2 inch binding, you need more than the 1/4" seam. It should be around 3/8". When you turn the corners you need to stop stitching at 3/8" for that perfect corner miter. Then fold and pivot as usual.
Are you able to move your needle on your machine? For my BL machine the setting is -3.0 for a 3/8" seam and the -2.75 is a shy 3/8" seam. I keep these settings on a small card by the machine.
Make some samples to try with your machine. Record the settings right on the samples for future use.
I stitch to the BACK first and bring around to front and use a decorative blanket or feather stitch on the front. It's easy to see where the stitches are as I sew. The back is already down and if the stitch line is off a bit on the back, no worries. My machine has a laser light so that helps me stitch a straight line.
Good luck!
PS: My quilter did the binding(by machine) on my last two quilts, easy and done. I had the quilt labels already made and she stitched those right into the binding at the corners. It was wonderful to receive completed quilts!