Here is a practical chart, taken from the American Screen Printing Association's website, that any screen printer can use when choosing mesh counts. It will give you an idea of what mesh count to use for each printing job.
4 Mesh – Glitter inks 30 Mesh – Shimmer/Crystalina inks
60 Mesh – Team Wear, player numbers, puff inks, metallic inks.
83 Mesh – Cold Peel & Hot Split transfers, heavy white underbase.
109 Mesh – Regular artwork with average details, no very fine lines or halftones
125 Mesh – Regular artwork with average details, no very fine lines or halftones
140 Mesh – Regular artwork with average details, no very fine lines or halftones
162 Mesh – Semi-detailed artwork, large halftones.
200 Mesh – Underbase for detailed prints, detailed artwork, halftones, index color.
230 Mesh – Very detailed artwork, halftones, index color
305 Mesh – 4 color process color printing, overprint colors for simulated-process, fine halftones, very detailed art.
These mesh counts apply to textile and hard goods as well. For printing with solvent based inks on ad specialty products, mesh counts of 230-305 will usually produce desired results as a thin ink deposit is usually indicated.
TIP: You do not need to have all of the mesh counts indicated on hand in your shop. If you are just starting out as a typical textile screen printer, a good starting point would be to order a mix of 83's, 109's, 162's, 200's and 305's.