I used to work for Teespring, so yeah, I know about them. I don't know as much about them now (it's been almost 3 years), but I think overall they're pretty good. I bought a shirt less than a year ago from them. There was a delay in it shipping out but the quality of the print was mostly okay (the registration was off slightly so a very little bit of white was showing under the red ink). The shirt quality is good.
I would definitely recommend using Teespring or a site like them since the iron on stuff isn't going to cut it. You may want to look around local businesses too. I don't know how they are, but I do see small t-shirt printers even in malls. You can ask what type of printing they do since they all have different specifications. Such as screeprinting, DTG, heat applied graphics or sublimation.
Some basic points... anything that could remotely be copyrighted is better to stay away from. It's also good to stay away from gradients and use flat colors. Screenprinting is the less colors the better. One or two colors will allow you the most bang for your buck since screenprinting pricing is highly determined on the number of screens used. Typically an all white design works well because it can go on a lot of different color shirts. Vector format file, if you can do vectors.
It's also good if you can make a design that could interest not only your fanbase but a wider audience as well. Easier said than done - good luck!