Impressions Magazine has really good articles on the business of screen printing. Here's their website Decorated Apparel Industry | T-Shirt and Garment Printing Business. I suggest looking at the articles listed under Build Your Business.
If you are wanting your logo out there or even an online banner and link check with the ones that sell the ads. You might be able to trade a print job for several things.
I did this with a local TV station recently that needed shirts for an event.