If you place your design on Zazzle and CafePress, they will handle selling it and distributing it. You should look into it and see what the margin is that you will receive.
Once you are set up on a site that handles sales and distribution, all of your online promotional materials (website, e-mail links, etc) can simply point to the URL's where the t-shirts can be purchased. That way, you don't have to spend all of your free time, packaging and shipping your products. This allows you to focus on marketing and sales.