The quest for the perfect tee is not really obtainable since tees are a reflection of the wearer's own personalities. But there are ways of getting closer to reaching the goal.
You maybe wanting to know what will make the perfect tee design and or blank for marketing purposes. For this market research is needed.
First, a survey is needed. "What is your favorite T-Shirt and why?". Based on some past surveys, a lot of times there is a memory attached to the tee, often associated with another person that the wearer knows.
Second, with the data break it down to what design was on the tee. Most will have some commercial design on it from some Movie franchise or Band Name or Tour. If the Tees are funny what is the joke, is there a common element to the humor tees?
Finally, take the most common elements from people's answers and try to combine them into something new. For instance if people loved their Guns N' Roses Appetite For Destruction tee, make a parody of it with something from the present time that people are currently into like the Firefly themed Appetite For Misbehavin tee
It may not replace their old favorite tee for sentimental reasons but it will definitely remind them of their old favorite.
Quest For The Perfect Tee.
Trying to replace people's favorite tee with a completely different is a quest of its own. For a tee that you hope to sell a ton of, combine the Survey with whatever is trending. Use the search Engine and current memes to get some ideas. Often Timing is everything. The more relevant something is to NOW the more likely people will be interested in it. These are called Topical Tees, but they typically lose their appeal once people move on from the subject matter. The ideal tee would be to combine it with something classic that isn't going away like the Mona Lisa.
That is how I'd pursue the perfect tee.