I tried using the zig zag first and wasn't pleased with the results. I couldn't control the density when I went around corners (operator error I am sure - lol). I settled on blanket stitch and had good results with it. I wouldn't hesitate to mix them up for interest.
The last applique I did - I tried sewing by hand with a tiny needle and very thin thread. I actually really liked the look and will try that again.