I use variegated thread in the bobbin all the time. It just depends on the backing. If my backing has multiple colors variegated thread blends better. Two tone and solid fabric I'll generally use solid matching color thread....
I have to admit the thread color just hits me while I am working on my project. I may have to audition several shades, but I generally just know what I want to use.
Good luck on your project and post pics when you get it done!