I would definitely applique first and quilt afterwards. The quilting can greatly enhance the applique.
If this is a large quilt, you could do it in sections (where you remove all but the middle third of the batting and quilt that first). There are a couple of books that explain how to do this, and it has been the subject of a few threads here.
For air, I'm thinking you could FMQ swirling feathers in a variegated blue thread on a white background. Or you could applique white clouds on a blue background, perhaps adding some birds riding on the air.
Water is an example of where an applique could be greatly enhanced by quilting. You could create an applique lake and quilt ripple patterns on it, or swirls. Or you could create a waterfall and quilt straight lines down the water fall and circles in a pool at the bottom.