Printing detailed greyscale photographs is something we frequently do at Monster Press. There are often 2 options for printing these, & which of these you choose depends on a couple of things; your budget & how accurate a reproduction you require. In this example we're going to use a high resolution wallpaper from a quick Google search (below).
This is the original image, probably not so great as a t-shirt design due to the square shape & cropped off edges (!), but for the purpose of this article it'll do. We chose this image as it has a lot of subtle shading & soft highlights. There are a couple of ways we could go about printing this, either using 3 screens: underbase white, grey, highlight white (below, left) or 1 screen: white ink on a black background (below, right).
As you can see the subtle shading in the image is reproduced much more accurately using 3 colours as opposed to just white ink. The version with just white ink is much brighter, with higher contrast. The blend between the darker shades & the solid black background is more drastic. The positive of the white print, is that it would be considerably cheaper than printing the 3 colour greyscale image, especially for lower quantities, so whichever way you want to go about printing your image depends on your budget.