When I'm doing applique on a quilt that will be used and washed often, I use the blind-hem stitch on my machine. It takes 3 straight stitches and one to the side to stitch over an edge. This way I know it will hold up in the washings.
If you are doing hand blanket stitching, I suggest you make a back stitch every 2nd or 3rd stitch so they are more secure. That's when you come up with your needle then go right back down over your thread to secure the stitches in place.
Good luck on your quilt and be sure to post a picture when its done.