DonnaReMe -- you've gotten a lot of good advice so far in this thread. Big round of applause for your first project!
I think what you are describing as a multipplae zigzag stitch is what I call a serpentine (some people call it snake too) stitch and it is one of my favorite techniques for quilting down a project. Let your machine do the work and you get a slightly more interesting design, while allowing for some wobbles and such not only in your quilting but your piecing as well. It will, as you mentioned sort of refer back to the overall pattern.
As Bkay suggested, I'd go along the diagonal lines all the way through the border and off the edges. I sure hope (however you do it) you will be able to post a picture of your finished project -- and that you stay here on the boards. I think you have a great attitude and keep in mind one of our sayings around here, done is better than perfect!