For a mechanical engineer, most ‘apt’ MBA could be ‘operations management’, as OR is closely related, and could help mechanical engineers to apply the techniques to shop floor, operations and in field. Supply chain management is offered in few colleges, and is also apt for mechanical engineers.

At tier-1 and 2 colleges however, courses in demand are Finance and marketing, at the end of the day, there is no ‘best’ course, depends on your interest, aptitude, temperament and passion. My advice is not to venture into MBA unless it is in Tier-1 or at least Tier-2 colleges. Attempt CAT or GMAT after at least a couple of years work experience, select reputed college to join, after all you could afford to wait, as you are already employed.