The Confederacy was organized in February of 1861, more than half a year before Breckinridge threw in his lot with the Confederacy. The only way you'd see him as President of the Confederacy is if a major POD had caused all the border states to secede at the same time as the Deep South states (perhaps Chase got the Republican nomination?). I have always thought, though, that if Breckinridge had been made Secretary of War in 1862 rather than 1865, the Confederacy's odds of victory would have been significantly better.
Benjamin is a non-starter. The Confederacy would not go for having a Jewish president.
Robert Toombs is the most likely contender. Indeed, had it not been for a bad drinking bout in a hotel lobby during the Montgomery Convention, he might have ended up as President instead of Davis (which will be a minor plot point in House of the Proud). Toombs's weaknesses extended beyond his drinking, however, in that he tended to put ideology before pragmatism. On the other hand, he had an extremely solid grasp of fiscal policy, which would have served the Confederacy very well, as its own disastrous fiscal policy IOTL was a major contributing factor to its eventual defeat.
Robert Hunter of Virginia would be an interesting choice. He was one of the most prominent prewar politicians who joined the Confederacy and had been a highly effective legislator, but was quickly overshadowed by Davis once the war got going.