When I applique, I don't want the stitches to show so I use the color of the applique I'm piecing.... not the background color. I use a blind stitch and you don't see the stitching. Of course, you need a lot of colors but for me that's not a problem.... I must have 100's of spools of thread that I've gotten over the years. If it's really old, I pull off the 1st layer of thread. I've never had a problem with the thread breaking, even for very old threads.
Yes, do let us see your blocks. I'm really wanting to do a sunbonnet sue quilt..... just need to get some of those pesky UFOs finished.