How to output woocommerce products to a page, style and modify the html structure

To create a product listing page on your site, you just create a normal page in the admin. Then in the admin go to WooCommerce > Settings > Products > General and select that page for the “Shop Page” setting.

If you want a custom product page you could do basically what your saying above. Create a new page in the admin, say its called My Products. Then you could use a page template called page-my-products.php and you could include your query in that template.