If you want someone to wear your shirt (or promote your company through any free merch) then you might as well spend a little more and give away something great! In the case of shirts, I am a huge fan of the companies that give away American Apparel shirts instead of something crappy.
Companies that I've seen give away American Apparel shirts include:
Even when the company is a competitor to my employer (MailChimp), I'm likely to wear the shirt.
Companies that at least make a comfortable shirt without crappy graphics may still be worn after I'm through the American Apparel shirts.
Like in software, even if you are giving away something for free, you should focus on quality.