Just my personal opinion, but I agree that each crewmember will need a primary and at least one secondary skill like they have in Special Forces "A" teams. Perhaps it's best to think of the needed skills for a successful Mars mission and then attempt to assemble a crew around those skills.

Pilot - while most of the flight will be automated, you need someone with the necessary skills to monitor the various mission operations and take corrective action as necessary. We need to allow for the weakening in the crew as a result of long periods of weightlessness, so the actual piloting will probably be minimal.

Engineer - you need someone (or more) with the skills to fix just about anything. "Junkyard Wars" types come to mind. Stuff is going to break. That's a given. It has to be designed to be repaired in flight, something NASA has been weak at in the past.

Doctor - perhaps not only an MD but also a microbiologist/pathologist to help perform the search for life portion of the mission.

Scientist - need someone with multiple scientific skills including geology, meteorology, etc.

I believe a 4 person crew would probably be the practical minimum. Since they would have years to train for the mission, they could be cross trained adequately to keep the critical skills (engineering/medical/piloting in that order) available should any one of the crew be killed or injured. Prima-donna test pilot types need not apply.