What is the correct type of mattress to look for?

I'm 90 kg and 6 ft 1 inch, and share a double bed with a divan base with my wife. We've had a couple of mattresses that have caused me lower back pain. First a spring mattress from John Lewis and most recently a Simba mattress which we are returning. I'm looking for an alternative, a mattress that is very firm but which won't sag and which won't lead to lower back pain. I know it's a matter of taste, but what types of mattress would you advise me to consider.