You can't embed Shopify into WordPress. They used to have a plugin but that has been scrapped.

Currently the best way to have a WordPress ecommerce store that sells physical products is to use the free WooCommerce plugin from WooThemes.

It allows you to receive payments from PayPal.

As you will be shipping products you will need a shipping plugin - this will depend on which postal service or courier you are using to ship, e.g. Australia Post or UPS. These shipping plugins are not free. Have a look at the official list here https://woocommerce.com/product-category/woocommerce-extensions/shipping-methods/

That's probably the minimal set up you need to start to sell your T-Shirts and hats.

There are of course a lot more WooCommerce extensions that will enhance your store and your customer experience.

Hope that helps.
Wil.