Consider these 3 options:
Affiliate market for existing store sites for about 15% commission, ni inventory/shipping hassles.
Create a virtual "store" on a print on demand site like Zazzle.com or Cafepress.com, you just upload art, set prices, let them take payment and ship the product, Prices are high but may be a good way to test the market interest in your designs.
Make your own site, set up shopping cart, payment processing, invest in an inventory to get volume print price breaks and facilitate quick delivery. Handle order packing, shipping.
A few suppliers
All over shirt prnting
$4.95 shirts imagemarket.com
spreadshirt.com, Customink.com more shirt printers
You could seem more artistic using a local screen printer making prints you can feel, who makes each one a bit different.