If you suffer from back pain, then choosing the right mattress is very important. The important thing is to maintain good spinal alignment. This means your body maintains a broadly straight line from your head down to your shoulders and back, through to your hips, knees, and feet.
If you lie a mattress that's too soft, you'll sink in the middle and that line will become a curve. Conversely, if a mattress is too firm, your hips and shoulders won't sink in enough when you turn onto your side.
Unfortunately, what constitutes "too soft" or "too firm" varies from person to person, so finding the right balance is very much a case of trial and error. A latex mattress is definitely worth trying, though, as they're generally firm, helping to keep the spine aligned, while the natural bounciness of latex can help reduce pressure points and improve circulation.
Most importantly, while changing your mattress may help with back pain, this won't by itself solve it, so it's important to consult with a medical professional or physical therapist about any spinal issues.