using multiple shipping carriers and delivery types will require some hand coding to accomplish. I would suggest signing up for a Premiere support appointment to help with this.
On the checkout page, you would need to add a select list to choose the carrier, and another to choose the delivery method.
Different carriers offer different delivery methods, so the delivery method select list options will need to change based on the selected carrier.
On the confirm page, you would need hidden elements for each select list, to capture the selected options from the checkout, use the same names as the select lists for the hidden element, also, you need to add Set Session Value behaviors to store the selected carrier and delivery method.
you would need to add a shipping lookup behavior for each of the carriers offered in the carrier select list. and set the delivery method to use the method select list.
In the shipping rules, add a rule for each carrier, use trigger for based on session value to trigger the appropriate shipping rule based on the selected carrier.