Your runner is beautiful! Love the print you decided to use for the border! If you use one of the fabrics you mentioned for the backing -- the aqua print or the grayish silver print -- for the backing, then I would turn it to the front as the binding. Not sure which fabric you mean that's in the pineapple, but that mottled silvery lilac that is the lower right hand triangle of the block that encloses the center square would look smashing, I think.
Whatever you do, it will look stunning.
Sorry, no recommendations on the quilting. I'm a novice in that department myself.