If merchandise is going to be used to promote a product, it is a good idea to examine how you are going to execute this strategy. If a shirt, sticker, or coffee cup has just a logo on it, this is usually done by marketers to reinforce brand name recognition. Linux Mint needs to promote in order to break out of the "Techie Only" to find real growth in a consumer market. Those consumers need to be informed what Linux even is. Otherwise, this promotional merchandise will just be cool to the inner circle of it's already won fans. Trying to gain brand name product recognition to those unfamiliar with it, does not work very well.
I think Linux Mint is such a great product that needs to be demonstrated to others outside the present fan base. Evangelism should be geared toward winning new converts.
To that end, there is going to be a difficulty in doing this. I saw an interview with Linus Torvalds and he made some good points. He said Linux on the desktop will only win, when it is preloaded on machines.http://youtu.be/KFKxlYNfT_o
I agree with Linus Torvalds. Knowing this, I would aim promotional gear toward potential OEM's that would preload Linux Mint on their hardware. I would try to get makers of commodity PC's interested too. These OEM's try to sell their systems into the largest market, consumers. This is the hardware that will buy the games from companies like Valve. Valve is porting their steam platform and games to Linux. Hopefully Linux on the desktop will gain momentum.
Successful promotion is not going to be easy to figure out. But it looks like some long awaited opportunities for desktop Linux might be finally happening.