There is a preference to take a bath as part of the chafifah (and this is cited by halachic authorities as the accepted custom), since soaking will allow the water to reach into all the folds and crevices of your body better than showering, it will help loosen any dirt better, and it will help soften scabs and other hardened/rough areas.
However, according to most authorities, a thorough shower is acceptable if there is a need (unavailability of a bath, difficulty with a bath, medical reasons, etc.). You should just take care to shower very thoroughly, paying close attention to all the folds and crevices of your body.
There is no minimum duration for the bath or shower. You have to determine what is the normal time it takes for you to thoroughly clean yourself without feeling rushed. 15-20 minutes seems to be reasonable; however, it may take longer or shorter for you depending on how long it takes you to wash and comb your hair, whether you have to shave, how clean your nails and feet are, etc.
Please feel free to get back to us with any further questions.