Okay, a human captain. What about the first officer? I see two routes we could go down.
a) Human, or another Federation alien: This will give the series a very 'Star Fleety' feel. This might be good if we want to keep the ship on Star Fleet's good side, which some of these ideas would need to keep the series going.
OR
b) An alien of a threat species or an alien with very different outlook: Help give the series a less 'clean' look. I don't think Star Fleet would likely make use of, or trust as much if, say a Cardassian or Romulan were in positions of power. This might, however give us more shows that go into the ship's dealings with foreign powers.
Each side has lots of benefits and drawbacks. It all depends on what 'type' of show we are creating.
On the Cardassian Crewman: I think we should have a Cardassian on board. It will be hard to justify, though. Why would a Cardassian run off and join a mixed ship when there has to be plenty of Cardassian only merchant ships? Could be an interesting dark secret behind it.