Welcome ... Grinch ... how seasonal of you to choose that name!
It's really your personal preference.
As much as some will tell you that you should use a blanket stitch,
many will tell you that a zig-zag is the way to go!
Another factor to consider is how close together your stitches are,
and how deeply they go into the appliqued fabric.
Then, there is always the double stitched zig-zag or blanket stitches to consider.
Also, a full on satin stitch to consider as well.
You didn't say whether you are doing raw edge applique or turned applique.
That would make a difference re the hold-up-ability when laundered,
no matter which type of stitching you choose.
All this being said, you might want to do a test piece with the same fabrics, and applique methods you are using on your quilt. Try the different stitching options and make your decision. Then launder it a bunch of times!
And always keep in mind .... it's your quilt, and you need to do it the way you want to do!!!