Hi there! This is a great question - I actually started an apparel company that sells through Etsy about a year ago. We looked in to quite a few different fulfillment options, and, because of that, I've developed a really extensive list of resources and companies to do this. The answer to this really comes down to how much you want to spend per shirt, as well as the quantity of each design you want to order.
Some companies use a process called Direct to Garment which allows you to order one item at a time as orders come in. This process is usually more expensive overall, but you don't need to order a bunch of the shirts before you know if they will sell through. Your margins are reduced though, and you need to wait for the shirts to be printed before shipping them, adding to the turnaround time after each order.
Another option is Screen Printing, which can get you much lower costs per shirt, but you need to order in much higher quantities. This method is great if you have only a few designs that you are trying to sell, but becomes less feasible with more designs.
As I said before, I have a really extensive list of companies that I've tried, so I know which ones really provide great quality, which ones are lower cost, and which ones do direct fulfillment. Let me know if you want to talk more!
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