Make the tension as balanced as you can. Sometimes the thread will sink into the middle more after washing. Otherwise, you could use a monofiliment thread. Every quilt is different. Usually people pick backing fabric based on what color thread they're going to use, but I've seen a lot from my applique guild where people match/coordinate to the front & don't worry about the back (using same color in top & bobbin). Others say that combining W&N with Hobbs wool (or wool blend) helps to bury the peaking threads. Some set the thread tension so that the front thread will peek on the back, but not the reverse.
It's your quilt & your artistic decision. If it were my quilt, I'd see how white thread looks doing that front & back. If I didn't like that, I'd go with red for both and not worry about the back.