How does Commerce handle product prices and sales tax/VAT?
Taxes in Commerce are quite flexible. They are organised around Tax Groups (each product is assigned to one tax group) and Tax Rules (each Tax Group can have many rules, processed top-to-bottom until the conditions meet) that determine the charged tax rate. By using different rate providers, you can either specify tax rates manually, or rely on an up-to-date database of VAT rates across the European Union and integrations with TaxJar or Avalara (subscription required) for the more complex US Sales Tax rates.
In terms of your product prices, you can configure them to be either inclusive or exclusive of taxes. The difference is wether the taxes will be added on top of your product price in the cart, or if the taxes are essentially deducted from your product price. Depending on your target market or local regulation, one of these options is the most approviate.
If your in a territory/market where product prices are exclusive of taxes, you can use the render_taxed_price snippet to show inclusive prices based on the customers' country, which will evaluate your tax rules to show the same total price the cart would show.
To show the right tax amounts before the customer enters their address details, use the Default Address or AutoFill GeoIP modules to set a default state/country to use.
Read more about configuring your tax rules in the documentation.