Look at the colors you are using and pick a color thread that coordinates with as many of them as possible. If i use lots of blues and greens a teal coordinates nicely. If its lots of reds, pinks, yellows, oranges, then a peachy tone works well. If its reds, pinks, purples, blues, then some shade of purple would likely work.
Then when you are attaching the background I would go on and use thread to match the background.
This way you are only using two or three different threads and still don't have to worry about undue thread visibility.