yes for more detailed with will need something other then screenprinting i am wondering the same thing...how to get photos printed onto a shirt.....
you can host your story with bigcartel ...shopify and alot of others
halftone (consist of dots to make shadows. The bigger the dots the darker the print, smaller more spread dots make shades and greys)
index printing (4-6 screens color separated to make colors from mixtures of the basic colors CYMK. The arrangements of the dots will make shadows and what not. Online companies can be paid to make these separations for you and for cheap depending on who you go with. Most printers will charge you $45+ a hour for art fee's for something like this. Better to outsource)
DTG (unlimited colors. Only limited to what ink the printer takes. No bright colors, glow in the dark and fluorescent colors either)