You don't specify machine or hand quilting thread. I am assuming for quilting by machine. Questions:
1. Do you prefer a matte finish or a shiny thread?
2. Do you prefer the thread to show or just want texture to show?
3. Are you a fiber "purist" or are you ok with synthetic fiber threads (ie not 100% cotton)
4. Why only white? If you want something that seems to play nice with everything and doesn't fight with other colors in the quilt, white isn't always the best choice, but if you seem to only use white as your neutral or background color when piecing, then I suppose it would make sense to only consider white.
5. Assuming machine quilting; are you quilting on a domestic, longarm or midarm?
6. Are you opposed to a different thread in the bobbin than what you are running on the top?
I use many different threads, many different weights, colors and fiber content. For me to suggest what I use would be a long list and most likely offer no help to you. I can offer better recommendations if I know a bit more.