I'm not sure how big your blocks are, but I'd probably do the corners of the blocks and the centers. I have used both crochet thread and regular yarn-either works well (some people even use narrow ribbon, but I'd worry that it would fray). You might look for a bright, variegated yarn since you have many colors. I use a darning needle--it works for me even on the thicker parts. I also use the surgeon's knot.