Tricot, quiana, silk and, to a lesser extent, kettle cloth and light cotton blends, will show great print detail. The process for printing fabrics is much the same as that used to print paper. It is a good idea to first experiment on a scrap of the fabric you will use to see how it will accept the ink. Some fabrics need more ink, some less, for an effective print. Always wash the fabric before printing it.
Washing removes the sizing and makes the print colorfast.
I use oil base block printing ink on fabric because I can control it best. I have experimented with acrylics, but find that they dry out too fast. Water base inks are not colorfast and so cannot be used on anything that will be put in water. You can achieve some interesting effects with artist's oils if time is not important. They can take weeks to dry.