EDIT: 4) I'm thinking about a large US military cargo plane painted in company colours. Would a civilian model be better?
For non-oversized cargo the 747 just can't be beat - it dominates large global air trade because it's just that good, but it is being replaced with the 777, which is better.
For larger cargos (larger vehicles), Lockheed offered commercial versions of the C-141 and C-5, but both were turned down on fuel use costs. The MDD/Boeing MD-17 (commercial C-17) died because by the time it was around the thousand or so IL-76s and few dozen An-124s had the market cornered.