For most of the T-shirt printing, 110 Mesh will be good for you. If you need to do some finer detail use 155 Mesh or above. 280 Mesh or 305 Mesh is for you to do the 4-color process. The 40 or lower mesh count will be needed when printing some glitter's ink.
A general rule: The finer the detail of the graphic, use higher mesh count.