Stephanie here from Shopify's guru team!
You don't need to worry about setting up proper tax rates with Free Shipping. As long as you have your physical presence[s] set up and your products are set to charge taxes, orders should be taxed appropriately. You can, however, select whether or not you would like to charge tax on shipping rates under "Settings" > "Shipping".
I would recommend giving our doc on setting up taxes in the US a read! Here it is: https://help.shopify.com/manual/taxes/usa-tax-settings
While we can't guarantee 100% accuracy with regard to which taxes apply to your business specifically, we always recommend reaching out to a tax professional to ensure you're doing everything you need to do :)
Hope this helps!