Pretty block! It depends on what stitch you will be using. If satin stitching, I plan out which shape is under the next shape and stitch the background pieces first. Since the next color of satin stitching covers the start and finish of the thread under it, I don't have to worry about the thread tail until the last piece on top. Those I leave long, knot and bring to the back.
If I am using a buttonhole stitch, I knot and bring the threads to the back with each thread colour.
OR you can use one of the new invisible threads and use the same thread for a tiny zig zag and knot and bring the thread tails to the back.