The best mattress for back sleepers is one that keeps your hips in a neutral position. This can be anywhere between medium and firm depending on your weight. However make sure you avoid soft mattresses.
The key area to focus on is your hips. Side sleepers also need to think about the shoulders and neck but this is not so much of an issue for back sleepers. The reason why the hips are an issue is that the firmness of the mattress determines whether they are kept in a neutral position.
If the mattress is too firm and the hips are not allowed to sink into the neutral position they will be held too high. This means the natural arch in your back will be flattened. If the mattress is too soft then the back will arch too much as the heavy pelvic bones will sink too far into the mattress.
Medium firm is a good bet but adjust towards firm or medium as your weight dictates. If you have a small natural arch then you can tend towards firmer, if you have a larger natural curve tend towards softer. A back sleeper can generally handle a firmer mattress compared to a side sleeper.
Many mattresses offer zoned lumbar support. This is something to look for if you are a back sleeper. If you have a firm support layer you can get a softer upper layer or pillow top to provide that comfort and ability for the pelvis to sink in.
In terms of material the best mattress for back sleepers are latex or memory foam. Avoid spring mattresses as when you put your weight on them they push back against you are can create pressure points on your lower spine.