What is the best position to sleep in for my back pain?

Great suggestions already! I also suggest investigating your mattress. Mattresses should be replaced every 7-8 years. If you notice a human sized divot in your mattress, maybe sooner. When shopping for a mattress, usually the most comfortable ones in the store are too soft to spend 7-9 hours laying on at night time. Err towards the firmer mattress as this will provide your spine with more support as you sleep, and can help reduce the need for pillows.

What you are doing sounds excellent. Have your spine in a NEUTRAL position, that is comfortable and supported.

Some people who are side sleepers like having the leg that is on top a little in front of the bottom leg. That leg is supported by the pillow. It takes the pressure off your lower back. This is a favorite position for women who are pregnant.

What is the nature of your back pain? Do you know the primary cause and does the pain mainly show up at night? I think Karen Buck's ideas are great for sleep - you could also incorporate some day time strategies for back pain relief if you know what the cause of it is.

As Dr. Cook mentioned, sleeping on the unaffected side with a pillow in between the bent knee (flexed) helps. But, the type of pillow is important. The objective is to neutralize the angle of the gluteal muscles (which are leg lateral rotators) so that the upper leg is parallel with your mattress. The pillow should be wide and long so that the ankles are also supported for the greatest benefit. Sometimes a small pillow or rolled up towel under the waist can realign the low back spinal column for positional release of the lumbar muscles. Just to start your sleep in this position can help as we all do move around.
Also, a pillow under the knees can help with back sleepers. To promote sleeping on the back, a small soft pillow on the tummy can promote security and flatten the lower back for relaxation. There are total body pillows available or just one specific for side lying positions.
Stomach sleeping is the least beneficial for the low back and neck.

Side sleeping and lying on your back are the two best positions to sleep in, especially for back pain. If you have one side that is more effected than the other, you could try laying on the opposite side with your hip flexed to take some stress off the low back. Ex...pain on right side, lay on left side with right leg flexed at the hip and on a pillow. You could also look into some anti-inflammatory supplements to decrease the discomfort and improve sleep quality.