Hi nichicara,
There is no specific type of mattress that would be best for a rotator cuff injury so I would follow the same steps in the mattress shopping tutorial as for any other mattress purchase except if you sleep on your side I would especially make sure that the mattress is soft enough under your shoulders to allow your shoulders to sink in enough and reduce pressure on the torn rotator cuff if you sleep on that side (and I would also avoid sleeping on that side for extended periods of time). I would also make sure that you choose a suitable pillow that keeps your head and neck in good alignment to help reduce some of the tension and pressure on your shoulder and it would also help to sleep with a pillow in between your arm and torso on the side of the injury which can also help prevent tension on the tendon.
Phoenix