Make all Shipping Methods Available to set as Default Shipping Method

The Default Shipping Method can be set at Setup > Site Builder > Set Up Web Site > Setup tab.

If shipping items are not showing on the dropdown field on the Set Up Web Site page, these shipping items are not set to be displayed on the web store.

1. Navigate to Lists > Accounting > Shipping Items.
2. Edit any shipping item then see if Display in Web Site is checked.
3. If the Display in Web Site box is not present on the record, the Charge for Shipping option is not enabled.
4. To enable it, go to Setup > Accounting > Shipping.
5. Check Charge for Shipping then click Submit.
6. After enabling, go back to the Shipping Item and the Display in Web Site and other options such as Shipping rate, etc. will be displayed.