For tee shirts, just sign up for Merch by Amazon. You upload your designs, they handle everything once a sale has been made.
https://merch.amazon.com/landing
There is a process to get accepted, but it is pretty simple. It took them about 2-3 months to accept me. I'm not even a designer, just signed up on a whim. Never followed through with it even--I wonder if I am still considered a partner...