Default tax rate
The first one in the list will be the default. You can re-order these by clicking and dragging using the "hamburger" (three lines) on the far right.
Tax Exempt Customers
You can make a customer Tax Exempt by navigating to the Customer Detail tab of the customer you wish to make exempt and select 'Edit'
Next click the 'Additional Tabs' button along the top
Scroll down and you can check the 'Tax Free' check box.
Remember to click the green 'Update Customer' button to save the changes. The customer will now be tax exempt on transactions.