I don't know the Singapore market, but here in the US there are many specialty/boutique shirt sites offering shirts at various price points. My opinion is that you'll come out better, at least starting out, finding things people are already talking about and making shirts related to those concepts. Snorg Tees and other shirt companies in the US do this, often taking movie lines, Internet memes etc. and designing shirts around them (while being careful to stay on the right side of trademark issues.) They also have "in house" designs, but the ones that they tend to advertise -- and probably the bulk of their volume -- comes from the ideas they pick up around the 'net and from other media.
Many print-on-demand services exist for shirts, but you may find that the margins you make on orders, particularly if you dropship as well, are so thin to be barely worth the effort (unless you are doing truly massive volume.) Price shop aggressively.
"Failure is not when you fall down. Failure is when you don't get back up."