Great video overview of how to start a t-shirt business with shopify.
In shopify you can use print on demand companies that take care of all of your printing and shipping. You end up making less profit in the beginning per shirt but you have no up front costs or inventory which can be costly when you start out.
What I really like about doing this through shopify is you are growing your brand. It’s your site, its your designs, the shipping has your brand logo on it. So when you do want to screen print your own shirts its as simple as switching it over to your own inventory.