I would continue the pebbling quilting for all the white portions, blocks, borders and sashing. I think that having a different quilting texture/design would get busy and detract from the pop of color you are going for.
I would probably keep the border and just add a binding, probably a solid, though it could be fun to make every join a design opportunity and put a small block of color at random places. I would audition the various binding options and photograph -- then take a look at them on a computer screen and see what looks best to you.
A trick that can help with getting a wall hanging to lie flat and hang well -- before you bind it, go around the edges with a wide zig zag stitching to secure the layers, wash it, then dry it flat, and block it out nice and square. If you have some distortion, you can trim it up at this point. then add your binding and hanging sleeve (consider placing a sleeve top and bottom and putting a dowel in the bottom to weight it. It will also allow you to switch which end is up, which can reduce wear and possible fading. I've also been known to encourage a wavy wallhanging to straighten up by using a few strategically placed old sewing machine needles directly through the quilt and into the wall at various points. The tip of a needle doesn't make a hole worth noticing in the wall, and obviously it's been through the quilt sandwich many times with no drama, so unless the safety of children or pets is an issue, I find it a good way to recycle old needles.