Mesh from about 28 to 60 is generally considered extremely coarse, making it suitable for shimmers and metallic ink, which allows relatively large pigment particles or flakes to pass through the mesh open area without clogging. It's also used for overcoats and caviar beads.
Mesh from 83 to 140 is used for the majority of athletic work, where you want a lot of ink and opacity. The workhorse mesh selection in this area is 110. A mesh count of 140 to 200 is the medium range of mesh, with 156 probably the most commonly used in the industry.
Mesh counts from 173 to about 195 are used for detailed printing that still requires a large ink deposit, while anything above 200 is used for fine detail and halftones.
It's extremely rare to see anything printed on a mesh count above 355 in the textile industry.
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That would basically work, although it won't give you the exact mesh count that's actually available for sale (but near enough if you have an order form with a list in front of you).
For practical applications:
110 or 125 for white ink on dark shirts
140 or 125 for light color shirts
160, 180 to 305 for very fine detail
I have 70+ Newman Rollers and probably half are 125s - that's what i use most.
plastisol inks 
