I just happen to be reading 'Embattled Rebel' by James McPherson - a very well-written analysis of President Davis' leadership during the War.

In it he says that Davis had expected the job to go to Howell Cobb of Georgia but that the convention at Montgomery had chosen Davis specially because of his military background. People seem to disregard his extensive military experience these days: West Point graduate - 1828. Served seven years in various Army posts and fought in the Mexican-American War as a Colonel. Was recognized for bravery at Buena Vista and was wounded there. Served as Secretary of War under Franklin Pierce. Chairmen of the Senate Commitee on Military Affairs. In January 1861 he was named a Major General of the Army Of Mississippi - a job he coveted.

Davis had expected to be offered the position of General-in-Chief of the Confederate Army by the convention and did not want the Presidency but he had a strong sense of duty and accepted. He worked tirelessly and his health suffered greatly during the war because of the long hours he kept and the stress of dealing with all of the minutae of dealing with military matters. He was a very hands-on although somewhat reluctant President.

Both Bell and Breckenridge came from states that had not joined the Confederate States at the time of Davis's election, moreover Bell had ran as a Unionist Candidate in the 1860 election.