WordPress consultant & developer. WordPress Sydney meetup group co-organizer. WordCamp Sydney organizer. WordPress Australia Steering Committee member. Conference speaker. Business Mentoring.
If brand is hugely imporant to the business you are trying to build and the .com domain is already in the same industry as you are trying to break into, you will likely struggle with SEO for the .net domain.
If your business is not competing in the same industry or niche as the .com then it's fine to buy the .net domain.
SEO and traffic have nothing to do with the Top Level Domain (TLD).
If you have a bog standard ecommerce store and don't need to do anything fancy or stand out of the crowd now or in the next 5 years then Shopify is a good choice for you.
If you've seen something on another ecommerce site that Shopify doesn't have and you think you may want to grow your business to use it then I would seriously look at investing in WordPress with WooCommerce now. It is not easy to move from boxed solutions like shopify to something else.
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.