an advantage to having many 'likes' is it makes your site look active and that a lot of people are interested in your product. you get them to your FB or twitter, then hope you can lure them into your main site for the actual purchase. and i don't think it costs that much, so as far as getting your name out there, it's probably a fairly good investment.
imo, the first order of business is having a great website. that's where everything happens, the end result of directing people hither and yon on the net. it's where you make your sales. everything else is pointless if your site isn't professional... or at least able to conduct business through. i think this is also where the vast majority of would-be captains of the shirt industry fail, by having cheezy, poorly designed sites that aren't in line with their market's expectations. almost invariably such failure is a result of not putting enough money into it and the naive, arrogant notion that somehow, despite all logic, statistical information, and dirth of business acumen and experience, their design is so strong it can overcome these obstacles. 'hey, i'm on facebook, what more do they want?!'
kick-*** website. facebook (most ppl serious about it are likely to try the ads at some point), twitter, printerest. good seo probably won't hurt. involve yourself in forums that your market segment goes to if that's applicable. some people send a shirt into a t-shirt blogger for a review.
but, where people are going to make a name for themselves, also, is in real life. not knowing your brand it's hard to suggest some things.
...and give it time. don't be discouraged if you don't make a sale in your first three months.