My feeling is if you are going to give something let it be something that a person would not throw out and really brands you in a way that makes you stand out and be special. A tee-shirt to me is common and if it's branded it's not likely I would put it on my body.
However if you gave me a water bottle from S'well with your logo on it - that puppy would be with me everyday and I'd be thinking about the fact that you were someone who cared enough to give away something really special.
Just my thoughts....