Super smash bros differentiates between fast and slow movements of the analogue stick.
A + slow move of stick > attack in that direction
A + fast move of stick > SMASH attack in that direction
slow move up > nothing
fast move up > jump
slow move left/right > walk
fast move left/right > start sprint
SO when the stick is mapped to keys, you can't control how fast a movement is simulated (please, more experienced users, correct me if I'm wrong).
The C-buttons are an alternative jump button. Mapping your keyboard to a C-button to jump should work fine.
For other features, try mapping the analogue stick to the mouse. A game pad with an analogue stick is probably best to use but I assume you don't have one.