What is a good, recommended bed to relieve back pain?

Depends. No specific bed has been shown to be helpful. Different people prefer different beds so try a bunch out and see what's most comfortable for you. If your bed is too old though it may be time to replace it.
Controversial. There is no scientific studies to determine which beds are best for the relief of back pain. There are many good studies that show that weight loss, stretching, and core strengthening (via exercise) are good long-term treatments for back pain.