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.

I agree about using WooCommerce - but you also might consider going on a bigger platform if you have a lot of inventory. WooCommerce has a plugin that allows you to sell items that are on Amazon through your website. If you are selling your own inventory you can ship to Amazon FBA and also advertise your niche product on your store. If you do not want to sell your own inventory you can also sign up to be an affiliate on Amazon - then link your WooCommerce store to the affiliate links, earning additional money on products that you are not responsible for shipping. There are a variety of strategies depending on your market. Let me know if you need more details, happy to help!

Having worked with all ecommerce platforms I agree woocommerce is best in terms of using directly as a plugin with wordpress.

I don't necessarily agree it is the best out of the box shopping cart that can be used with wordpress however.

You could put the store in a subdirectory of the wordpress site and use any out of the box software my favorite as the most professional with tons of plugins available is either prestishop or zencart. This would provide a lot more possibilities.