First, it’s beautiful!
Once the top is done, give it a good pressing and measure it. Then you’ll know what size you need your batting and backing to be. The batting should be a few inches larger than the top on every side. The backing fabric should be just slightly larger than the batting. Most quilt batting is cotton or a blend, and fairly thin. So, you’re not in much danger of creating something too heavy and suffocatingly warm if you stick to that (I like warm & natural brand, and dislike pellon since it shredded on me during a pre-wash).
Making sure that everything has been ironed, then you pin your layers together. I do mine like this, and have never had an issue:
Lay down your backing fabric, wrong-side up. Smooth it out and pin the edges to your carpet (or tape to a hardwood floor, I suppose). Line up an edge, and lay your batting down on top of that. Very gently smooth out any wrinkles. Again, lining up an edge, lay down your topper, and smooth. Pinning - I like to start in the center and gradually move towards the edges. Remove the floor pins and it’s stable enough to move around now.
Once it’s pinned, I found that a giant quilting hoop worked well enough for hand-stitching, removing pins as I would move the frame. If you’re lucky enough to have one with a stand or a quilting frame, that’s a bonus. Again, I like to work from the middle outward but I think it’s safe to start at one edge. The batting will tell you the maximum amount of space between stitching that will remain stable…it’s usually about 8"-10".