The absolute star of this quilt is the applique. If I were to LAQ one I would SID around the applique elements and do a background fill where needed to get the applique to pop. Either fill with pebbling, echo quilting, swirls or some other element. I would quilt in the same color thread as my background fabric so as not to detract in any way from the star of the show.
If I were to hand quilt I would again, SID around the applique and most likely a simple cross hatch in the background where needed in a 1" or smaller grid. Many of the blocks in this quilt don't leave much space for quilting anything but a SID outline of the gorgeous applique and embrodery.