http://en.wikipedia.org/wiki/US_presidential_election,_1868
The only acceptable choice here is Grant IMO due to his commitment to enforcing civil rights legislation in the South.
I would have voted for Grant. As you note, he seemed like the obvious choice at the time. His faults as a political leader wouldn’t be revealed until he was in office.
Grant, clearly, but he needs to have able AND honest advisors. He’s a soldier, not a politician.