I use YLI hand quilting thread. It's glazed and quilts very nicely. I buy it online at Red Rock Threads or at Uncommon Threads - if you google them you'll find the website, and some quilt shops carry it, too.
The only times I have had trouble with breaking and fraying was when I used machine quilting thread. I also had a spool of Coats and Clark that had slubs and thin spots.
Janet