The way I look at the role of a medic, I would class it as that of an orderly or lab assistant, albeit one that has been trained in more that just first aid. Their main job is to assist the doctors and nurses in their duties on the ship. The training that they would have received would be considerably higher than that of a first-aider by today's standards. After all, the technology is considerably higher, and as the computer diagnosis' most illnesses and injuries, I would think that they would be allowed to treat minor problems. Of course in emergency situations they are allowed to treat patients to stabilize them in order to get them to a doctor.

Other major roles of the medic are labwork, and the care of the equipment. The medic would be able to perform simple lab duties such as blood and DNA analysis, and other similar tests. The responsibility of caring for the equipment would also fall on them. They would be responsible for the storage, the cleaning and the diagnostics of it.

The role of the nurse is not too far different from that of the medic. The differences are the medical tasks they do. Their main task, apart from aiding the doctors in treating patients, is the welfare of the patients in sickbay. They carry out the routine treatments on the patients, whether they are in or out patients. Their training would be more advanced than that of a medic, but in their quiet periods, they would assist the medics in caring for the equipment.

As mentioned before, this is the role most people take on. It is less restrictive on duty, as the doctor can carry out all the tasks of nurses and medics and much much more. This is the character I would recommend you choose.

Unless you are a strong role-player, I would recommend you choosing the Doctor. The other two roles will require much on your behalf, as it would be up to you to find things to do not the GM.