ACMoore carries a silk screen printing kit for around $50. I bought mine from them a while back. You can print anything you want including t-shirts. Just make sure you use ink specifically for use on fabric. It's a lot of fun!
I think you are caught up in a vocabulary change which will confuse most younger people as it does me.
Transparency is something that is laid down on an overhead projector to show an image.
Screen prints are captures of a computer screen
I think you mean
Screen prints are made in "silk screen" printing where the image is transferred by wiping ink across a fabric surface where the pattern is blocked out so the image only is allowed through in some places.
I also think (not being deep into this process)
That the industry has completely changed and now uses photographic development of screens using UV lamps or sunlight and negatives which are printed on transparent plastic using low cost (up to a certain size) laser or ink jet printers.