I would measure all the pieces and write those measurements down, incicating whether the piece is directional or not. I would also audition the fabrics to see if any of them don't work with certain other ones.
Option 1: I play with graph paper. First I mark the finished backing size you need (remember you want the backing to be larger than the finished top) on the graph paper and then puzzle the other sizes into that outline. I usually just pencil mine in but I have cut pieces of post it notes and placed them in the outline. Eventually, I end up with a layout that works.
Option 2: Just pick pieces that have the same dimension along one side (or trim one to match the other) and sew them together. Add on in the same manner until one row is done. Make a second row and so on until you have a backing.
I press the seams on the backing open to keep bulk down.