There's no such thing as a "best" martial art. Different martial arts have different emphases, so one style might be better for one person, but a poor choice for somebody else. If you're recovering from a rotator cuff surgery, which martial art is the best choice will depend on your stage of recovery and your goals for taking up this particular form of exercise. Whatever form you choose, don't start until you have clearance from your doctor and physical therapist.
Avoiding Injury
During the early stages of recovery from a rotator cuff surgery, your highest priority is avoiding re-injury. For these purposes, non-contact martial arts that don't heavily involve the arms are the wisest choice. Tai chi, silkreeling, and qigong are examples of this kind of martial art. If you're athletically minded, you might look into a leg-intensive style like tae kwon do or tang soo do, although many classes in those arts include heavy contact with training targets or classmates.
Rebuilding Strength
If you're reached a stage in your recovery where rebuilding your shoulder strength is a priority, you should look into martial arts that emphasize the muscles in and around your shoulder. Capoeira, jiu jitsu, judo, kenpo and boxing are some choices that suit this purpose. Bear in mind, though, that the same work that builds muscle can also risk re-injury. Listen to your body and stop any activity that seems to be making things worse instead of better.
Self Defense
Protecting yourself and the people you love doesn't stop being important just because you're recovering from an injury. In fact, some people feel the need to take martial arts classes because they've become physically compromised. If you fit this description, your best bet is a style that stresses combative effectiveness without an accompanying emphasis on physical conditioning. This maximizes the skills you learn while keeping your shoulder away from undue strain that could affect your healing. Combative training that meet this criteria include krav maga, haganah and Fast Defense.
Culture and Instruction
Different instructors may teach the same style very differently. So, you may enter a school where the culture of the class is very different from what you'd been led to expect -- such as a tai chi class that emphasizes combat and impact. If you find a school where that's the case, consider looking into other programs until you find one that teaches martial arts in a style that matches your recovery needs.
Common Sense Caution
If you're like most people, you want your shoulder to recover fully and remain a functioning joint. This means taking care of it during recovery. Only start martial arts -- or any other exercise program -- after a rotator cuff surgery with the full knowledge and consent of your doctor. Check in with your doctor frequently, and don't get "macho" about training through the pain. If something hurts your shoulder, stop doing that thing.
