Dynamic change of Shipping methods

When checking out there is an option of shipping method. How can I change those? My problems are:

  1. Regardless the selection of the payment method, the shipping method options show the same thing. For example, I select the Credit card, the shipping method still show the UPS Ground COD option.

  2. How to change the shipping charge and to make it reflected in the final price?

    Thanks for your help,