There is no one-size-fits-all answer to this question, as the best mattress for a person with a bad back depends on the individual's specific needs and preferences. (Good answer)
Some people find that a firmer mattress is better for their back, while others prefer a softer one. Memory foam, latex, and innerspring mattresses are all options to consider. It is important to try out a mattress before making a purchase, as it is difficult to know for sure what will be comfortable without giving it a test run. (Good answer but know that with memory foam that solution will not last as long as with latex and May last as long as with coil construction)
Some mattress stores have a return or exchange policy that allows you to test out the mattress for a period of time before deciding if it is the right one for you. (Good answer and know that visiting a store to try out the comfort levels of mattresses dramatically reduces the chance you'll need to exchange for a different model)
Alternatively, you could try purchasing a mattress online from a company that offers a trial period or a return policy, so that you can test it out in the comfort of your own home. (While true, it will just be a fluke if you pick the right mattress. I don't care if a mattress model has 1000 five star reviews those clearly happy people aren't you and don't have your body type)