I like this question! Where all my frugal people at?
Sublimated Prints and Screen Prints are considered to be the ones that would last longest. Screen printing has been around for a long time, so there are many different variations of it.
Screen printing is the most popular form of t-shirt decoration, especially with slogans and cartoons. The colors of these shirts will eventually fade over time, but there are still a lot of these available.
You can also use your screen-printing skills to print t-shirts with a special design on them. A screen print shirt would also be very durable, as the ink is heat-cured. It is meant to stand the test of time. By that, we mean that these shirts should be able to go through the washing machine at least 50 times (the general industry standard) before the print wears away, and usually the print will last quite a bit longer than that.
One option that is growing fast in popularity is t-shirt sublimation. Instead of placing the ink directly onto your material, the ink goes through a special nozzle that sends it through a hole in the T-shirt material. After that, it is printed directly onto the t-shirt. So, you would literally have to rip the shirt to shreds in order to lose the print.
Obviously, a lot of different factors will affect that timeline (washing your clothes with bleach, for instance, will dramatically reduce the life cycle of your custom printed shirt). Bottom line: follow the care instructions on the label!