I use one strand of good quality thread. I do the lock stitch on the needle (you pierce the thread) so the needle stays threaded and do a quilter's knot on the end. There are YouTube videos on how yo do them.
When hand stitching my binding to the back, every few inches I put a knot into the sandwich so if the thread breaks, only a small section comes out. I like to sew my corner miters down as I go and I also bury a knot at each corner. With all my starts and stops, I pop the knot through the fabric and end the thread into the sandwich.