The characters which I used throughout of FFVI consisted of:
Sabin: Did large amounts of damage with his blitzs attacks, also saved my life many times in tight situation.
Cyan: Awesome Sword techs, they also saved my life many times.
Celes: I recall her being able to absorb magic damage or something like that? it's been too long to remember but the unique ability to her was very useful, she was an excellent asset to the team.
Shadow: Although throughout most of the game you never really 'got' him in your party untill the end he proved most useful throughout all the times you got him. His throwing techniques did large amounts of damage and thus allowing you to defeat your enemy with ease.
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