I always iron mine down first and then pin or glue-baste it down before stitching. It helps me to maintain a more even binding width on the front and a straighter fold. I don't have any problems with stretching, but it's something to watch for...
As you can see, quilters have different methods that work well for them, so feel free to experiment a little and see what works best for you.
Congrats on getting ready to finish up your quilt!