What would be your strategy?

Do some Pinterest marketing: create an account, post some great pictures of funny t-shirts, give them noteworthy titles, follow the big hitters in your niche.

Get a Twitter bot and start following people who follow other big t-shirt manufacturers. Regularly interact with them and post conceptual photos of t-shirts that have the potential to be retweeted and go viral.

Do some inventive Twitter marketing. Off the top of my head ... let's say a sports star gets involved in an off-the-field controversy. Design one of your t-shirts with a slogan mocking the star (like a meme), then tweet the picture to the top talkers about the subject, such as sports writers and broadcasters. A retweet from a single top tweeter could bring in enough traffic to crash your server!

Set up Google Blog Alerts to notify you anytime a keyword related to your t-shirts is mentioned. Then go and make an informed, breezy comment on the blog with a link to the t-shirt for which the post is relevant.

Just some thoughts to get you started. Riff off 'em.

This is something very interesting as there are lots of things you have to do for making a good fan page. Lets talk about a strategy how you make friend around you and what type of social person you are? if you are good in your social life than treat facebook just like that you will see many people comes to you.

Facebook has recently added a feature through which products can be bought directly from the Facebook page itself.

i would make a video with all the tshirts
and i would offer a good price
research keyword about your product
in your video put the tilte and in the tags
make a lot of backlinks to your video and put it on the first page of gogle
after you will get a lot of clients

I think you should create some attractive photo albums with good captions. You can even tag your friends to get noticed.