Someone is going to definitively say 305 mesh 
Because you're asking, I'd first say you should do a WHOLE lot of reading on process printing, the theory behind it, it's limitations, print technique, set up, inks, separation and everything associated with it.
I say that because there are a lot of elements involved each of which alone can create issues. From inadequate art and separations to light sources, emulsion choice, screen coating and image/halftone burning, to mesh selection, set-up and print technique.
To more directly answer you inquiry, there is no "best" anything. What kind of "photograph" shirts are you planning? How accurately do you want them reproduced? What kind of press/colors do you have?
The assumption is that the higher the mesh and detail, the better. But it depends on the look you want, the art and other factors. And actually the overall goal should be using as coarse a mesh and large dot as possible to get acceptable results (which is subjective). I suggest starting with lower mesh counts (126, 156) to get comfortable with burning and maintaining halftones, then working up to finer counts. Process has limitations which can be compensated for in different ways, but high end process usually requires additional colors to round out the color gamut necessary. There are different angles that can be effectively used to minimize undesireable moire and maximize image clarity. And some use same angles for all colors. Then there's the choice of round dots, elliptical or diamond (square) all of which can produce different but great results. The inks are pretty transparent and require proper cure like conventional plastisols so a heat press will do.
Because you're asking, I'd first say you should do a WHOLE lot of reading on process printing, the theory behind it, it's limitations, print technique, set up, inks, separation and everything associated with it.
I say that because there are a lot of elements involved each of which alone can create issues. From inadequate art and separations to light sources, emulsion choice, screen coating and image/halftone burning, to mesh selection, set-up and print technique.
To more directly answer you inquiry, there is no "best" anything. What kind of "photograph" shirts are you planning? How accurately do you want them reproduced? What kind of press/colors do you have?
The assumption is that the higher the mesh and detail, the better. But it depends on the look you want, the art and other factors. And actually the overall goal should be using as coarse a mesh and large dot as possible to get acceptable results (which is subjective). I suggest starting with lower mesh counts (126, 156) to get comfortable with burning and maintaining halftones, then working up to finer counts. Process has limitations which can be compensated for in different ways, but high end process usually requires additional colors to round out the color gamut necessary. There are different angles that can be effectively used to minimize undesireable moire and maximize image clarity. And some use same angles for all colors. Then there's the choice of round dots, elliptical or diamond (square) all of which can produce different but great results. The inks are pretty transparent and require proper cure like conventional plastisols so a heat press will do.
