You will find all the verified children clothes wholesalers you need there.
Iron on transfers will fade over subsequant laundrings, but, with great care, will last much longer.
However, a good silk screen will outlast the shirt, itself.
The EASIEST, less messy method is iron on transfers. This is especially true of designs of more than one color.
So the choice is more a matter of need than of preference.
For example, I used to do custom airbrushed tee shirts at craft fairs and boutiques. For the more popular patterns, I found that cutting stencils from manila folder stock was a great time saver. And, for working out on a site where electricity and running water was not available, was the ONLY choice.