I took a great binding class when I worked with a quilting group. Now there are lots of YouTubes available.
When I am machine finishing the binding I sew the binding to the back of the quilt, iron out the binding away from the body of the quilt, turn the quilt over and iron the binding back into the quilt. At this point I can use school glue or glue stick if I want. Then I stitch. Due to the preironing there is no stretching required to make it all fit. I sew with one fo my 'fancy' stitches.
When I am going to hand bind then I sew the binding to the front of the quilt, iron away from the body of the quilt, turn it over, iron back to the body of the quilt on the back. Again I can use school glue or glue stick if i want. I find I only use 1-2 of the small wonder clips as I hand sew because I can easily remove and replace them. The joke is buy a pack of 10 and share them with 5 of your best friends.
The ironing seems like a lot of time but it makes everything else go so much easier and faster.