The thread color will really depend on the effect you're trying to achieve.
If your desire is for the applique to be the focus, you could use an invisible thread. The quilting patterns will still show though, the the main focus would remain the applique.
If your desire is to accent the quilting, then a contrasting color thread is your best bet.
A thread color matching the applique background fabrics will be similar to the invisible, but you may need to change thread colors for each applique background, if they're not all the same. The stitching will show up more with the matching thread, than with the invisible.
And you can use different threads in the top and bobbin to achieve the desired effect. For instance on the last quilt I made for my DN, I used invisible on the top to keep the bargello pattern the focus. But I used a variagated cotton thread in the bobbin, to show off the stitching on the back of the quilt.
The choices are endless and reflect your individual tastes.